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Deep Reinforcement Learning Based on Search Space Independent Operators for Black-Box Continuous Optimization 认领 引用
1
作者 Ye Tian Yisai Liu +1 位作者 Shangshang Yang Xingyi Zhang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2026年第4期913-925,共13页
Deep reinforcement learning(DRL)has demonstrated exceptional capabilities in combinatorial optimization,which automatically devises policies for solution construction and optimizer refinement.DRL is particularly adept... Deep reinforcement learning(DRL)has demonstrated exceptional capabilities in combinatorial optimization,which automatically devises policies for solution construction and optimizer refinement.DRL is particularly adept in generating training samples by itself,thereby providing the flexibility to solve a variety of combinatorial optimization problems without supervision.While DRL takes actions according to states extracted from problem-specific information,it cannot be directly applied to black-box continuous optimization lacking explicit information.To address this issue,this paper proposes a search space independent operator based DRL method for black-box continuous optimization.It conceptualizes the optimization process driven by search space independent operators as a Markov decision process,wherein actions are defined as operators and states are extracted from solutions generated by operators.In contrast to other DRLassisted metaheuristics,the proposed method does not rely on any existing metaheuristic.Instead,it innovates by creating totally new operators,able to surpass the performance boundaries of existing metaheuristics.Compared with state-of-the-art metaheuristics and DRL methods,the proposed method shows significantly faster convergence speed on challenging continuous optimization problems. 展开更多
关键词 Black-box optimization continuous optimization metaheuristic reinforcement learning search operator
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Intelligent Safe Optimal Control Towards Koopman Operator-Driven Nonlinear Systems With Asymmetric State and Input Constraints 认领 引用
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作者 Yalu Su Ding Wang +3 位作者 Mingming Zhao Dan Xiong Yiyong Huang Wei Han 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2026年第5期1135-1150,共16页
For unknown nonlinear systems subject to asymmetric state and input constraints simultaneously,this article establishes a safe value iteration paradigm to learn an optimal control policy in a data-based manner.Initial... For unknown nonlinear systems subject to asymmetric state and input constraints simultaneously,this article establishes a safe value iteration paradigm to learn an optimal control policy in a data-based manner.Initially,the Koopman operator,instead of the black-box neural network,is applied to extract the inherent dynamics of the controlled systems from the measured data,thereby allowing for explicit analysis of the prediction error.To tackle the issue posed by state and input constraints,a crafted control barrier function is seamlessly incorporated into the canonical utility function,which retains the property of positive definiteness for the asymmetric case.Moreover,the value iteration algorithm with regard to the augmented utility function is adopted to attain a safe optimal controller,where the actor and critic networks are leveraged to approximate the control input and associated value function,respectively.The monotonicity,safety,and stability of the raised algorithm are further verified rigorously.Via performing three experiments on the linear system,the nonlinear system,and the manipulator plant,comparative results are obtained to substantiate the superiority and efficacy of the developed approach in achieving optimal performance and safe guarantee. 展开更多
关键词 Adaptive optimal control constrained value iteration control barrier function discrete-time nonlinear systems reinforcement learning Koopman operator
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Boundedness of Pesudo-differential Operators on Besov Spaces 认领 引用
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作者 DAI Jiawei LU Yanfei +1 位作者 ZHENG Ruxiu HUANG Qiang 《数学进展》 CSCD 北大核心 2026年第3期578-588,共11页
In this paper,we investigate the boundedness of pseudo-differential operators Tαon Besov spaces Bp,qswith symbol a∈Sρ,δm,0≤ρ≤δ<1.We obtain that Tαis bounded from Bp,qs+m-mc(p)to ... In this paper,we investigate the boundedness of pseudo-differential operators Tαon Besov spaces Bp,qswith symbol a∈Sρ,δm,0≤ρ≤δ<1.We obtain that Tαis bounded from Bp,qs+m-mc(p)to Bp,qs,where■. 展开更多
关键词 pseudo-differential operator Besov space Hörmander class
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MEAN LI-YORKE CHAOS FOR A SEQUENCE OF OPERATORS ON BANACH SPACES 认领 引用
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作者 Jian LI Xinsheng WANG Jianjie ZHAO 《Acta Mathematica Scientia》 SCIE CSCD 2026年第3期1187-1207,共21页
In this paper,we obtain the dichotomy between mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space.The mean Li-Yorke chaos for sequences and ... In this paper,we obtain the dichotomy between mean equicontinuity and mean sensitivity for a sequence of bounded linear operators from a Banach space to a normed linear space.The mean Li-Yorke chaos for sequences and submultiplicative sequences of bounded linear operators are also studied.Furthermore,several criteria for mean Li-Yorke chaos are established. 展开更多
关键词 linear operator mean Li-Yorke chaos absolutely mean irregular vector mean equicontinuity mean sensitivity submultiplicative sequence
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BOUNDEDNESS OF THE BERGMAN TYPE OPERATOR Tλ,τ,c,k,k′FROM Lp(BN,DVα)TO LQ(BN,DVβ) 认领 引用
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作者 Xuejun ZHANG Min ZHOU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第2期812-825,共14页
Bergman type operators are closely related to many basic problems on operator theory and function space theory.In this paper,we characterize the boundedness of logarithmic Bergman type operator Tλτc,k,k′from L^(... Bergman type operators are closely related to many basic problems on operator theory and function space theory.In this paper,we characterize the boundedness of logarithmic Bergman type operator Tλτc,k,k′from Lp(Bn,dvα)to Lq(Bn,dvβ)for some 1≤p,q≤+∞ and real α,β.These results generalize the relevant work of some scholars.At the same time,we partially solve the problem,put forward by Chen et al.in JMAA(2024). 展开更多
关键词 logarithmic Forelli-Rudin type operator weighted Lebesgue space integral estimate boundedness unit ball
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THE BOUNDEDNESS OF INHOMOGENEOUS CALDERÓN-ZYGMUND CONVOLUTION OPERATORS ON LOCAL PRODUCT HARDY SPACES 认领 引用
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作者 Shaoyong HE Jiecheng CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期99-111,共13页
It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and t... It is well known that the inhomogeneous Calderón-Zygmund convolution operators are bounded on the local Hardy spaces.In this paper,we prove that these operators are bounded on the local product Hardy spaces and the Lipschitz spaces.The key ideas used here are the discrete local Calderón identity and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense. 展开更多
关键词 local Hardy space Lipschitz space inhomogeneous Calderón-Zygmund operator discrete Calderón identity
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The Characterization of Self-adjoint Domains of Two-interval Odd Order Differential Operators 认领 引用
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作者 WANG Linyu HAO Xiaoling LI Kun 《数学进展》 CSCD 北大核心 2025年第4期784-802,共19页
In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval... In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals. 展开更多
关键词 self-adjoint domain odd order differential operator two-interval
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Direct and Inverse Approximation Theorems for Linear Combinations of Szász-Mirakjan-Durrmeyer Operators in Orlicz Spaces 认领 引用
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作者 Han Lingxiong 《数学理论与应用》 2026年第2期80-90,共11页
This paper investigates approximation problems in Orlicz spaces generated by Young functions.Utilizing Jensen’s inequality and the equivalence between the K-functional and the modulus of smoothness,we establish both ... This paper investigates approximation problems in Orlicz spaces generated by Young functions.Utilizing Jensen’s inequality and the equivalence between the K-functional and the modulus of smoothness,we establish both direct and inverse theorems for approximation by linear combinations of Szász-Mirakjan-Durrmeyer operators in these spaces. 展开更多
关键词 Direct theorem;Inverse theorem;K-functional;Orlicz space;Szász-Mirakjan-Durrmeyer operator
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Improvement of a Dual-Polarization Radar Operator for Ice-phase Microphysical Terms 认领 引用
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作者 Ji-Won LEE Ki-Hong MIN GyuWon LEE 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2026年第3期550-564,共15页
Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can en... Dual-polarization(dual-pol)radar variables provide information about the quantity,type,size,and water content of hydrometeors.Assimilating these dual-pol radar variables into numerical weather prediction models can enhance forecast accuracy.Observation operators are essential for radar data assimilation.This study focuses on applying a realistic dual-pol radar observation operator to more accurately calculate dual-pol radar variables.Previously reported dual-pol radar observation operators tended to overestimate radar variables near 0℃ in convective precipitation and simulate unrealistic dual-pol radar variables in subfreezing regions.To address this,the improved operator(KNU dual-pol radar observation operator;K-DROP)limits the distribution of mixed-phase hydrometeors,which have both solid and liquid properties,in areas with strong updrafts and downdrafts,improving the overestimation of radar variables near the melting layer.Additionally,by applying the observed snow axis ratio during winter to K-DROP,the issue of differential reflectivity(ZDR)being calculated as a constant value in subfreezing regions has been improved.By incorporating the observed maximum radius of hydrometeors into K-DROP,the overestimation of reflectivity(ZH)in subfreezing regions,the overestimation of ZDRin warm regions,and the underestimation of specific differential phase(KDP)in subfreezing regions and overestimation in warm regions,are improved.Compared to previous operators,the enhanced version reported in the present work produces more realistic dual-pol radar variables. 展开更多
关键词 dual-polarization radar operator observation operator radar data assimilation remote sensing
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Neural Operators with Adaptive Spectral and Low-Rank Representations 认领 引用
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作者 Nikita Sakovich Dmitry Aksenov +1 位作者 Ekaterina Pleshakova Sergey Gataullin 《Computers, Materials & Continua》 SCIE EI 2026年第9期2204-2222,共19页
Neural operators provide a data-driven framework for learning mappings between function spaces and have shown strong performance in scientific computing and surrogate modeling.Existing architectures,however,typically ... Neural operators provide a data-driven framework for learning mappings between function spaces and have shown strong performance in scientific computing and surrogate modeling.Existing architectures,however,typically rely on a single representation of the input function—either purely pointwise,as in DeepONet,or purely spectral,as in Fourier Neural Operators—which limits their ability to simultaneously capture local variability and global structure.In this work,we propose NOASLRR,a neural operator that integrates three complementary branches within a unified DeepONet-style formulation:a pointwise MLP embedding,a spectral branch based on Chebyshev polynomial coefficients,and a low-rank linear embedding.The three representations are fused through two learnable sigmoid gating mechanisms that adaptively balance structured inductive biases against unstructured expressivity in an input-dependent manner.We provide a theoretical guarantee showing that the proposed architecture can uniformly approximate any continuous operator admitting a decomposable structure,and we validate the method on three canonical PDE benchmarks:the heat equation,the viscous Burgers equation,and the Laplace equation with Dirichlet boundary conditions.On all three benchmarks NOASLRR converges faster and reaches substantially lower mean squared error than DeepONet and FNO baselines—for the heat equation the final MSE is reduced from 1.1×10⁻³(DeepONet)and 2.9×10⁻²(FNO)to 3.4×10⁻⁴,with comparable improvements on the Burgers and Laplace equations.Ablation experiments further confirm that each of the three branches contributes to the accuracy gains,while the parameter overhead relative to DeepONet remains moderate thanks to the low-rank factorization. 展开更多
关键词 Neural operators operator learning DeepONet spectral representation Chebyshev polynomials low-rank approximation adaptive gating partial differential equations
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An implicit adaptive Fourier neural operator for long-term predictions of three-dimensional turbulence 认领 引用
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作者 Yuchi Jiang Zhijie Li +2 位作者 Yunpeng Wang Huiyu Yang Jianchun Wang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第6期257-282,共26页
Long-term prediction of three-dimensional(3D)turbulent flows is one of the most challenging problems for machine learning approaches.Although some existing machine learning approaches,such as implicit U-net enhanced F... Long-term prediction of three-dimensional(3D)turbulent flows is one of the most challenging problems for machine learning approaches.Although some existing machine learning approaches,such as implicit U-net enhanced Fourier neural operator(IUFNO),have been proven to be capable of achieving stable long-term predictions for turbulent flows,their computational costs are usually high.In this paper,we use the adaptive Fourier neural operator(AFNO)as the backbone to construct a model that can predict 3D turbulence.Furthermore,we employ the implicit iteration to our constructed AFNO and propose the implicit adaptive Fourier neural operator(IAFNO).IAFNO is systematically tested in three types of 3D turbulence,including forced homogeneous isotropic turbulence(HIT),temporally evolving turbulent mixing layer,and turbulent channel flow.The numerical results demonstrate that IAFNO is more accurate than IUFNO and the traditional large-eddy simulation using the dynamic Smagorinsky model(DSM),while exhibiting greater stability compared to IUFNO.Meanwhile,the AFNO model exhibits instability in numerical simulations.Moreover,the training efficiency of IAFNO is 4 times higher than that of IUFNO,and the number of parameters and GPU memory occupation of IAFNO are only 1/80 and 1/3 of IUFNO,respectively in HIT.In other tests,the improvements are slightly lower but still considerable.These improvements mainly come from patching and self-attention in 3D space.Besides,the well-trained IAFNO is significantly faster than the DSM.Code and data available at:http://gffzz188fe103f8f1460askfn0vp0bfuqw60cb.ffgz.tsg.suse.edu.cn/yuchi-richard-jiang/IAFNO. 展开更多
关键词 Fourier neural operator Self-attention Turbulence Large-eddy simulation
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A neural operator-based hybrid microscale model for the multiscale simulation of rate-dependent materials 认领 引用
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作者 Dhananjeyan Jeyaraj Hamidreza Eivazi +3 位作者 Jendrik-Alexander Tröger Stefan Wittek Stefan Hartmann Andreas Rausch 《Theoretical & Applied Mechanics Letters》 EI CAS CSCD 2026年第2期185-193,共9页
The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales.To better understand the impact of microstructure on the macroscopic response,multiscale modeling st... The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales.To better understand the impact of microstructure on the macroscopic response,multiscale modeling strategies are essential.Numerical methods,such as the FE2-approach,account for micro-macro interactions to predict the global response in a concurrent manner.However,these methods are computationally intensive because of the repeated evaluations of the discretized microscale.This challenge has led to the integration of deep learning techniques into computational homogenization frameworks to accelerate multiscale simulations.In this work,we employ neural operators to predict microscale physics,resulting in a hybrid model that combines datadriven and physics-based approaches.This allows for physics-guided learning and provides flexibility for different materials and spatial discretizations.We apply this method to time-dependent solid mechanics problems involving viscoelastic material behavior,where the state is represented by internal variables only at the microscale.The constitutive relationships at the microscale are incorporated into the model architecture and the internal variables are computed on the basis of established physical principles.The results for homogenized stresses(<6%error)show that the approach is computationally efficient(~100×faster). 展开更多
关键词 Operator learning Multiscale simulation Heterogeneous microstructure Viscoelasticity Rate dependence
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TRUNCATED TOEPLITZ OPERATORS ON A CLASS OF QUOTIENT MODULES OVER THE BIDISK 认领 引用
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作者 Hong ZOU Tao YU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1581-1602,共22页
In this paper,we study truncated Toeplitz operators and little truncated Hankel operators on Np,q-type quotient modules over the bidisk.We find a necessary and sufficient condition for a truncated Toeplitz operator to... In this paper,we study truncated Toeplitz operators and little truncated Hankel operators on Np,q-type quotient modules over the bidisk.We find a necessary and sufficient condition for a truncated Toeplitz operator to be zero,as a result,we find a characterization equation for bounded truncated Toeplitz operators.We also find a necessary and sufficient condition for a little truncated Hankel operator to be zero operator.This paper also studies the spectra,joint spectra and the essential spectra of truncated Toeplitz operators with some special symbols. 展开更多
关键词 truncated Toeplitz operator little truncated Hankel operator Hardy space bidisk spectrum
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A Q-Learning Improved Particle Swarm Optimization for Aircraft Pulsating Assembly Line Scheduling Problem Considering Skilled Operator Allocation 认领 引用
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作者 Xiaoyu Wen Haohao Liu +6 位作者 Xinyu Zhang Haoqi Wang Yuyan Zhang Guoyong Ye Hongwen Xing Siren Liu Hao Li 《Computers, Materials & Continua》 SCIE EI 2026年第1期1503-1529,共27页
Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in oper... Aircraft assembly is characterized by stringent precedence constraints,limited resource availability,spatial restrictions,and a high degree of manual intervention.These factors lead to considerable variability in operator workloads and significantly increase the complexity of scheduling.To address this challenge,this study investigates the Aircraft Pulsating Assembly Line Scheduling Problem(APALSP)under skilled operator allocation,with the objective of minimizing assembly completion time.A mathematical model considering skilled operator allocation is developed,and a Q-Learning improved Particle Swarm Optimization algorithm(QLPSO)is proposed.In the algorithm design,a reverse scheduling strategy is adopted to effectively manage large-scale precedence constraints.Moreover,a reverse sequence encoding method is introduced to generate operation sequences,while a time decoding mechanism is employed to determine completion times.The problem is further reformulated as a Markov Decision Process(MDP)with explicitly defined state and action spaces.Within QLPSO,the Q-learning mechanism adaptively adjusts inertia weights and learning factors,thereby achieving a balance between exploration capability and convergence performance.To validate the effectiveness of the proposed approach,extensive computational experiments are conducted on benchmark instances of different scales,including small,medium,large,and ultra-large cases.The results demonstrate that QLPSO consistently delivers stable and high-quality solutions across all scenarios.In ultra-large-scale instances,it improves the best solution by 25.2%compared with the Genetic Algorithm(GA)and enhances the average solution by 16.9%over the Q-learning algorithm,showing clear advantages over the comparative methods.These findings not only confirm the effectiveness of the proposed algorithm but also provide valuable theoretical references and practical guidance for the intelligent scheduling optimization of aircraft pulsating assembly lines. 展开更多
关键词 Aircraft pulsating assembly lines skilled operator reinforcement learning PSO reverse scheduling
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Lp→LqEstimates for Stein’s Spherical Maximal Operators 认领 引用
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作者 Naijia Liu Minxing Shen +1 位作者 Liang Song Lixin Yan 《Analysis in Theory and Applications》 CSCD 2026年第1期90-108,共19页
In this article we consider a modification of the Stein’s spherical maximal operator of complex order a on Rn:■We show that when n≥,suppose||mα[1,2]f||Lq(Rn)≤C||f||Lp(Rn)holds for someα∈C,... In this article we consider a modification of the Stein’s spherical maximal operator of complex order a on Rn:■We show that when n≥,suppose||mα[1,2]f||Lq(Rn)≤C||f||Lp(Rn)holds for someα∈C,p,q≥,then we must have that q≥p and Reα≥σn(p,q):=max{1/p-n/q,n+1/2p-n-1/2(1/q+1),n/p-n+1}.Conversely,we show that Mα[1,2]is bounded from Lp(Rn)to Lq(Rn)provided that q≥p and Reα>σ2(p,q)for n=2;and Reα>max{σn(p,q),1/(2p)-(n-2)/(2q)-(n-1)/4}for n>2.The range ofα,p and q is almost optimal in the case when either n=2,or a=0,or(p,q)lies in certain regions for n>2. 展开更多
关键词 spherical maximal operators Lp-improving estimates wave equation local smoothing estimates
Koopman operator-based stable economic model predictive control for nonlinear systems 认领 引用
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作者 Jie Wu Ke Li Fei Liu 《Control Theory and Technology》 EI CSCD 2026年第2期250-259,共10页
This paper presents a data-driven economic model predictive control(EMPC)framework for nonlinear systems.Leveraging Koopman operator theory and the extended dynamic mode decomposition method,a lifted linear model in t... This paper presents a data-driven economic model predictive control(EMPC)framework for nonlinear systems.Leveraging Koopman operator theory and the extended dynamic mode decomposition method,a lifted linear model in the high-dimensional function space of the nonlinear dynamics is first identified from the collected dataset.Then,an EMPC strategy used to optimize process economics is designed in the lifted space,which employs the Koopman linear model as the predictor.To guarantee closed-loop stability,an artificial constraint is constructed by solving a convex quadratic programming problem.The recursive feasibility and closed-loop stability of the proposed approach are rigorously analyzed.Benefiting from the linear structure of the Koopman model,the online computational burden of the EMPC is substantially reduced.The effectiveness of the proposed method is demonstrated through simulations on a nonlinear chemical reactor. 展开更多
关键词 Closed-loop stability Economic model predictive control Koopman operator Recursive feasibility
A GENERALIZED HILBERT OPERATOR ACTING ON HARDY SPACES 认领 引用
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作者 Huiling CHEN Shanli YE 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期145-163,共19页
Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted... Letα>0 and letμbe a positive Borel measure on the interval[0,1).The Hankel matrix■with entries■induces,formally,the generalized-Hilbert operator■where f(z)■is an analytic function in D.This article is devoted to study the measuresμfor which Hμ,αis a bounded(resp.,compact)operator from Hp(0<p≤1)into Hp(1≤q<∞).We also study the analogous problem in the Hardy spaces Hp(1≤p≤2).Finally,we obtain the essential norm of Hμ,αfrom Hp(0<p≤1)into Hp(1≤q<∞). 展开更多
关键词 Hilbert operator Hardy space Carleson measure essential norm
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Estimates for p-adic fractional integral operator with rough kernels on grand p-adic Herz-type spaces 认领 引用
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作者 XIA Xiaoxi ZHOU Jiang 《中山大学学报（自然科学版）（中英文）》 CAS CSCD 北大核心 2026年第2期153-159,共7页
The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel Iβ,Ω′pand its commutators generated by b∈Λγ(Qpn)(0<γ<1)and the I_(β,Ω′... The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel Iβ,Ω′pand its commutators generated by b∈Λγ(Qpn)(0<γ<1)and the Iβ,Ω′p on grand p-adic Herz spaces. 展开更多
关键词 Lipschitz spaces grand p-adic Herz spaces p-adic fractional integral operator commutators
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THE STRONGLY SINGULAR CALDERÓN-ZYGMUND OPERATORS AND THEIR COMMUTATORS ON MUSIELAK-ORLICZ HARDY SPACES 认领 引用
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作者 Xiao WANG Wenchang SUN 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1643-1658,共16页
In this paper,we prove the boundedness of strongly singular Calderón-Zygmund operators and their corresponding commutators when mapping from Musielak-Orlicz Hardy spaces into Musielak-Orlicz spaces.By introducing... In this paper,we prove the boundedness of strongly singular Calderón-Zygmund operators and their corresponding commutators when mapping from Musielak-Orlicz Hardy spaces into Musielak-Orlicz spaces.By introducing a specific subspace of BMO,we further show that the commutators generated by functions within this subspace and strongly singular Calderón-Zygmund operators remain bounded under the same mapping framework. 展开更多
关键词 strongly singular Calderón-Zygmund operators commutators Musielak-Orlicz Hardy spaces
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Lipschitz Estimates for the Commutators of Fractional Hardy and Hardy-Littlewood-Pólya Operators on Grand p-adic Variable Herz Spaces 认领 引用
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作者 常云鹏 武江龙 《数学进展》 CSCD 北大核心 2026年第2期419-430,共12页
In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
关键词 p-adic field fractional Hardy operator Hardy-Littlewood-Pólya operator grand variable Herz space commutator
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