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GLOBAL WELL-POSEDNESSOF A PRANDTL MODEL FROM MHD IN GEVREY FUNCTION SPACES 认领 引用
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作者 Weixi LI Rui XU Tong YANG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第6期2343-2366,共24页
We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function s... We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2.The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator. 展开更多
关键词 magnetic Prandtl equation Gevrey function space global well-posedness auxiliaryfunctions loss of derivative
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MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES 认领 引用
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作者 林孝盛 杨大春 +1 位作者 杨四辈 袁文 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期484-514,共31页
Assume that L is a non-negative self-adjoint operator on L2(ℝn)with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝn satisfying som... Assume that L is a non-negative self-adjoint operator on L2(ℝn)with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝn satisfying some mild assumptions.Let HX,L(ℝn)be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝn)and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new. 展开更多
关键词 Hardy space ball quasi-Banach function space Gaussian upper bound estimate non-negative self-adjoint operator maximal function
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ON COMPACT COMPOSITION OPERATORS ON A CLASS OF HOLOMORPHIC FUNCTION SPACES OVER THE UNIT BALL IN C^n 认领 引用
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作者 龙素娟 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1367-1376,共10页
In this paper, a general function space X（B n ） over the unit ball in C n with norm · X（Bn） is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a comp... In this paper, a general function space X（B n ） over the unit ball in C n with norm · X（Bn） is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X（B n ）, related to works of [8] and [10]. 展开更多
关键词 compactness composition operator function spaces
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CHAINS OF FUNCTION SPACES OVER EUCLIDIAN SPACES AND LOCAL FIELDS 认领 引用
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作者 Zhaoxi Wang 《Analysis in Theory and Applications》 2009年第1期92-100,共9页
The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function... The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields. 展开更多
关键词 local field Lipschitz class function space morder continuous modulus morder Lipschitz class
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Coefficient Multipliers on Some Analytic Function Spaces 认领 引用
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作者 YUE Xiu-kui 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第3期344-351,共8页
In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞... In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (Hα∞, Hβ∞) = Hβ-α1 with 0 < α < β < ∞. 展开更多
关键词 analytic function space Hadamaxd product multiplier closed graph theorem operator
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ON THE SELECTION OF SHAPE FUNCTION SPACES OF TRIANGULAR PLATE ELEMENTS 认领 引用
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作者 陈绍春 《Acta Mathematica Scientia》 SCIE 1995年第3期275-282,共8页
Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.
关键词 unconforming finite element shape function space method of undetermined coefficients
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Regularity of Continuous Linear Operators on Banach Function Spaces 认领 引用
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作者 JIANGNian-shengt ChenZi-li 《Chinese Quarterly Journal of Mathematics》 2004年第1期51-56,共6页
In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.
关键词 Banach function space continuous linear operator regular
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ON VECTOR-VALUED FUNCTION SPACES WITH HELLY'S PROPERTY 认领 引用
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作者 Kazuaki Kitahara Toshinao Okada 《Analysis in Theory and Applications》 2001年第2期86-100,共15页
If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we s... If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class. 展开更多
关键词 Math ON VECTOR-VALUED FUNCTION SPACES WITH HELLY’S PROPERTY
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MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS 认领 引用
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作者 Zhu Yueping 《Approximation Theory and Its Applications》 2002年第2期65-71,共7页
In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Ha... In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces. 展开更多
关键词 Math MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS
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MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES 认领 引用 被引量：1
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作者 B.YOUSEFI Sh.KHOSHDEL Y.JAHANSHAHI 《Acta Mathematica Scientia》 SCIE CSCD 2013年第5期1463-1470,共8页
Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the... Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}. 展开更多
关键词 invariant subspace Hilbert space of analytic functions essential spectrum essential norm Fredholm operator multiplication operator
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Function spaces of Besov-type and Triebel-Lizorkin-type——a survey 认领 引用 被引量：3
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作者 YANG Da-chun YUAN Wen 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第4期405-426,共22页
This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
关键词 Besov space Triebel-Lizorkin space embedding atom molecule wavelet local mean Peetre maximal function dual complex interpolation
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Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces 认领 引用 被引量：6
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作者 Xianjie YAN Dachun YANG Wen YUAN 《Frontiers of Mathematics in China》 SCIE CSCD 2020年第4期769-806,共38页
Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As ... Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range. 展开更多
关键词 Ball quasi-Banach function space Hardy space finite atomic characterization Campanato space intrinsic square function
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Hardy Spaces Associated with Ball Quasi-Banach Function Spaces on Spaces of Homogeneous Type:Littlewood–Paley Characterizations with Applications to Boundedness of Calderón–Zygmund Operators 认领 引用 被引量：3
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作者 Xian Jie YAN Zi Yi HE +1 位作者 Da Chun YANG Wen YUAN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2022年第7期1133-1184,共52页
Let(X,ρ,μ)be a space of homogeneous type in the sense of Coifman and Weiss,and Y(X)a ball quasi-Banach function space on X,which supports both a Fefferman–Stein vector-valued maximal inequality and the boundedness ... Let(X,ρ,μ)be a space of homogeneous type in the sense of Coifman and Weiss,and Y(X)a ball quasi-Banach function space on X,which supports both a Fefferman–Stein vector-valued maximal inequality and the boundedness of the powered Hardy–Littlewood maximal operator on its associate space.The authors first introduce the Hardy space HY(X)associated with Y(X),via the Lusin-area function,and then establish its various equivalent characterizations,respectively,in terms of atoms,molecules,and Littlewood–Paley g-functions and gλ*-functions.As an application,the authors obtain the boundedness of Calderón–Zygmund operators from HY(X)to Y(X),or to HY(X)via first establishing a boundedness criterion of linear operators on HY(X).All these results have a wide range of generality and,particularly,even when they are applied to variable Hardy spaces,the obtained results are also new.The major novelties of this article exist in that,to escape the reverse doubling condition ofμand the triangle inequality ofρ,the authors subtly use the wavelet reproducing formula,originally establish an admissible molecular characterization of HY(X),and fully apply the geometrical properties of X expressed by dyadic reference points or dyadic cubes. 展开更多
关键词 ball quasi-Banach function space Hardy space space of homogeneous type Littlewood-Paley function Calderón-Zygmund operator
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Intrinsic Square Function Characterizations of Several Hardy-Type Spaces-a Survey 认领 引用 被引量：1
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作者 Xianjie Yan Dachun Yang Wen Yuan 《Analysis in Theory and Applications》 CSCD 2021年第3期426-464,共39页
In this article,the authors give a survey about the recent developments of intrinsic square function characterizations and their applications on several Hardy-type spaces,including(weak)Musielak-Orlicz Hardy spaces,va... In this article,the authors give a survey about the recent developments of intrinsic square function characterizations and their applications on several Hardy-type spaces,including(weak)Musielak-Orlicz Hardy spaces,variable(weak)Hardy spaces,and Hardy spaces associated with ball quasi-Banach function spaces.The authors also present some open problems. 展开更多
关键词 Intrinsic square function (weak)Musielak-Orlicz Hardy space variable(weak)Hardy space ball quasi-Banach function space Campanato space
Representation theorems of the dual of Lebesgue-Bochner function spaces 认领 引用 被引量：9
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作者 郭铁信 《Science China Mathematics》 2000年第3期234-243,共10页
By representing random conjugate spaces a general representation theorem on classical duals is proved. For application, we unify and improve many known important representation theorems of the dual of Lebesgue-Bochner... By representing random conjugate spaces a general representation theorem on classical duals is proved. For application, we unify and improve many known important representation theorems of the dual of Lebesgue-Bochner function spaces. 展开更多
关键词 random normed modules random coqjugate spaces representation theorems on classical duals LebesgueBochner function spaces
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On invariant function spaces HQ_p~q(R) 认领 引用 被引量：1
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作者 CHEN HuaiHui AULASKARI Rauno 《Science China Mathematics》 SCIE EI 2013年第10期1999-2006,共8页
New function spaces,which generalize the classical Dirichlet space,BMOA or also the recently defined Qpspace,are introduced on Riemann surfaces.Except inclusions between these generalized spaces it is shown that the c... New function spaces,which generalize the classical Dirichlet space,BMOA or also the recently defined Qpspace,are introduced on Riemann surfaces.Except inclusions between these generalized spaces it is shown that the capacity Bloch space is a maximal space for them. 展开更多
关键词 Riemann surface Green＇s function invariant function space
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The Dichotomy Between Traces on d-sets Г in R^n and the Density of D(R^n\Г) in Function Spaces 认领 引用 被引量：1
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作者 Hans TRIEBEL 《Acta Mathematica Sinica,English Series》 SCIE 2008年第4期539-554,共16页
A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are ... A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are introduced and calculated. 展开更多
关键词 function spaces d-sets fractals traces
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Some Properties of the Full Function Space and the Substitution Space 认领 引用
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作者 Zi Hou ZHANG Cun Yan LIU 《Journal of Mathematical Research and Exposition》 CSCD 2011年第5期887-897,共11页
In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the prope... In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained. 展开更多
关键词 full function space substitution space weakly sequentially complete bounded complete property （u）.
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Weak Hardy-type spaces associated with ball quasi-Banach function spaces I:Decompositions with applications to boundedness of Calderón-Zygmund operators 认领 引用 被引量：7
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作者 Yangyang Zhang Dachun Yang +1 位作者 Wen Yuan Songbai Wang 《Science China Mathematics》 SCIE CSCD 2021年第9期2007-2064,共58页
Let X be a ball quasi-Banach function space on Rn.In this article,we introduce the weak Hardytype space WHX(Rn),associated with X,via the radial maximal function.Assuming that the powered HardyLittlewood maxi... Let X be a ball quasi-Banach function space on Rn.In this article,we introduce the weak Hardytype space WHX(Rn),associated with X,via the radial maximal function.Assuming that the powered HardyLittlewood maximal operator satisfies some Fefferman-Stein vector-valued maximal inequality on X as well as it is bounded on both the weak ball quasi-Banach function space WX and the associated space,we then establish several real-variable characterizations of WHX(Rn),respectively,in terms of various maximal functions,atoms and molecules.As an application,we obtain the boundedness of Calderón-Zygmund operators from the Hardy space HX(Rn)to WHX(Rn),which includes the critical case.All these results are of wide applications.Particularly,when X:=Mqp(Rn)(the Morrey space),X:=Lp(Rn)(the mixed-norm Lebesgue space)and X:=(EΦq)t(Rn)(the Orlicz-slice space),which are all ball quasi-Banach function spaces rather than quasiBanach function spaces,all these results are even new.Due to the generality,more applications of these results are predictable. 展开更多
关键词 ball quasi-Banach function space weak Hardy space Orlicz-slice space maximal function atom molecule Calderón-Zygmund operator
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Upper(Lower) Monotone Coefficient of a Point in Orlicz Function Spaces 认领 引用 被引量：3
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作者 Hong Shi MA Xin Bo LIU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第5期585-598,共14页
The calculation expressions of upper （lower） monotone coefficient of a point in Orlicz function spaces are given.
关键词 Orlicz function space LM upper （lower） monotone coefficient upper （lower） locally uniform monotone point
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