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
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.
In this paper,we investigate the boundedness of commutators generated by theθ-Calderón-Zygmund operator with symbol function belonging to two kinds of weighted Campanato spaces.Specifically,we show that the comm...In this paper,we investigate the boundedness of commutators generated by theθ-Calderón-Zygmund operator with symbol function belonging to two kinds of weighted Campanato spaces.Specifically,we show that the commutators of theθ-type Calderón-Zygmund operator are bounded from weighted Lebesgue spaces to weighted Campanato spaces when symbol function belongs to weighted Lipschitz spaces;we also show that the commutators are bounded from weighted Morrey spaces to weighted Campanato spaces when symbol function belongs to a certain weighted Campanato space.展开更多
Let C be a conjugation on a separable complex Hilbert space H.An operator T on H is said to be C-symmetric if CTC=-T*,and T is said to be Cskew symmetric if CTC=-T*.It is proved in this paper that each C-skew sy...Let C be a conjugation on a separable complex Hilbert space H.An operator T on H is said to be C-symmetric if CTC=-T*,and T is said to be Cskew symmetric if CTC=-T*.It is proved in this paper that each C-skew symmetric operator can be written as the sum of two commutators of C-symmetric operators.展开更多
This paper considers compactness of the commutator[b,Iα]i(i=1,2),where Iαis a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author...This paper considers compactness of the commutator[b,Iα]i(i=1,2),where Iαis a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,Iα],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.展开更多
In this paper,the authors study the fractional Calderon type commutator TΩ,αAand its maximal operator MΩ,αAwith kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey...In this paper,the authors study the fractional Calderon type commutator TΩ,αAand its maximal operator MΩ,αAwith kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces Lp,λ(Rn).展开更多
In this paper,the authors prove that the parameterized area integralμΩ,Sρand the parameterized Littlewood-Paley gδ*-functionμΩ,δ*,ρare bounded on two-weight grand homogeneous variable Herz-Mo...In this paper,the authors prove that the parameterized area integralμΩ,Sρand the parameterized Littlewood-Paley gδ*-functionμΩ,δ*,ρare bounded on two-weight grand homogeneous variable Herz-Morrey spaces MKp,θ,q(·))α(·,λ)(ω1,ω2),where θ>0,λ∈(2,∞),q(·)∈B(Rn),α(·)∈L∞(Rn),ω1∈A_(p_(ω1))for p_(ω1)∈[1,∞]and ω2 is a weight.Furthermore,the authors prove that the commutators[b,μΩ,Sρ]which is formed by b∈BMO(Rn)and the μΩ,Sρ,and the[b,μΩ,δ*,ρ]generated by b∈BMO(Rn)and theμΩ,δ*,ρare bounded on MKp,θ,q(·))α(·,λ)(ω1,ω2),respectively.展开更多
In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,...In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.展开更多
Let Ω be homogeneous of degree zero,integrable on Sn−1 and have mean value zero,TΩ be the homogeneous singular integral operator with kernel Ω(x)/|x|n and[b,TΩ]be the commutator of TΩwith symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on Sn−1 and have mean value zero,TΩ be the homogeneous singular integral operator with kernel Ω(x)/|x|n and[b,TΩ]be the commutator of TΩwith symbol b∈BMO(Rn).In this paper,the authors prove that if sup ζ∈Sn−1∫Sn−1|Ω(θ|logβ(1/|θ·ζ|)dθ2,then[b,TΩ]is bounded on Triebel–Lizorkin space F0,qp(Rn)provided that 1+1/β−1<p,q<β.展开更多
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th...This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).展开更多
In this paper,we first introduce some new kinds of weighted amalgam spaces.Then we discuss the strong type and weak type estimates for a class of Calderόn-Zygmund type operators Tθin these new weighted spaces.Further...In this paper,we first introduce some new kinds of weighted amalgam spaces.Then we discuss the strong type and weak type estimates for a class of Calderόn-Zygmund type operators Tθin these new weighted spaces.Furthermore,the strong type estimate and endpoint estimate of linear commutators[b,Tθ]formed by b and Tθare established.Also we study related problems about two-weight,weak type inequalities for Tθand[b,Tθ]in the weighted amalgam spaces and give some results.展开更多
In this paper, we discuss the boundedness of commutators of high dimensional Hausdorff operator He on Herz type spaces. In addition, central BMO estimates for such commutators are also presented.
In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO(μ) functions on non-homogeneous metric measure spaces is obtained.
In this paper,the LP(Rn)-boundedness of the commutators generalized by BMO(Rn)function and the singular integral operator T with rough kernelΩ∈L log+L(Sn-1)is proved by using the Bony's formula for the paraprodu...In this paper,the LP(Rn)-boundedness of the commutators generalized by BMO(Rn)function and the singular integral operator T with rough kernelΩ∈L log+L(Sn-1)is proved by using the Bony's formula for the paraproduct of two functions.展开更多
Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The L^P boundedness of the nested commutators is proved on product space...Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The L^P boundedness of the nested commutators is proved on product spaces, where 1<p<∞.展开更多
In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley...In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^*- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.展开更多
In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and...In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.展开更多
Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multil...Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO(μ) functions.展开更多
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti...This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained.The vector-valued case is also considered.
基金partially supported by the National Natural Science Foundation of China(12171250,U21A20426,12271267)。
摘要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.
基金Supported by Chizhou University High Level Talent Research Start up Fund (No.CZ2025YJRC52)。
摘要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.
基金Heilongjiang Natural Science Foundation Joint Key Project(Grant No.ZL2024A001)。
摘要In this paper,we investigate the boundedness of commutators generated by theθ-Calderón-Zygmund operator with symbol function belonging to two kinds of weighted Campanato spaces.Specifically,we show that the commutators of theθ-type Calderón-Zygmund operator are bounded from weighted Lebesgue spaces to weighted Campanato spaces when symbol function belongs to weighted Lipschitz spaces;we also show that the commutators are bounded from weighted Morrey spaces to weighted Campanato spaces when symbol function belongs to a certain weighted Campanato space.
基金partly supported by the National Natural Science Foundation of China(Grant No.12i7195)by the National Key R&D Program(Grant No.2020YFA0714101).
摘要Let C be a conjugation on a separable complex Hilbert space H.An operator T on H is said to be C-symmetric if CTC=-T*,and T is said to be Cskew symmetric if CTC=-T*.It is proved in this paper that each C-skew symmetric operator can be written as the sum of two commutators of C-symmetric operators.
基金Supported by the Key Project of the Education Department of Fujian Province(JZ230054)the Sanming University's High-Level Talent Introduction Project(23YG09)the Natural Science Foundation of Fujian Province(2024J01903)。
摘要This paper considers compactness of the commutator[b,Iα]i(i=1,2),where Iαis a bilinear fractional integral operator,and b is a function in generalized Campanato spaces with variable growth condition.The author gives sufficient conditions for the compactness of[b,Iα],(i=1,2)from the product of generalized Morrey spaces to generalized Morrey spaces.
摘要In this paper,the authors study the fractional Calderon type commutator TΩ,αAand its maximal operator MΩ,αAwith kernels having some kinds of Log-type Dini-condition and obtain the compactness on Morrey spaces Lp,λ(Rn).
基金Supported by the National Natural Science Foundation of China(Grant No.12201500)。
摘要In this paper,the authors prove that the parameterized area integralμΩ,Sρand the parameterized Littlewood-Paley gδ*-functionμΩ,δ*,ρare bounded on two-weight grand homogeneous variable Herz-Morrey spaces MKp,θ,q(·))α(·,λ)(ω1,ω2),where θ>0,λ∈(2,∞),q(·)∈B(Rn),α(·)∈L∞(Rn),ω1∈A_(p_(ω1))for p_(ω1)∈[1,∞]and ω2 is a weight.Furthermore,the authors prove that the commutators[b,μΩ,Sρ]which is formed by b∈BMO(Rn)and the μΩ,Sρ,and the[b,μΩ,δ*,ρ]generated by b∈BMO(Rn)and theμΩ,δ*,ρare bounded on MKp,θ,q(·))α(·,λ)(ω1,ω2),respectively.
基金Supported by the National Natural Science Foundation of China(11671397,11571160,12071052)the Yue Qi Young Scholar of China University of Mining and Technology(Beijing)。
摘要In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.
基金Supported by NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
摘要Let Ω be homogeneous of degree zero,integrable on Sn−1 and have mean value zero,TΩ be the homogeneous singular integral operator with kernel Ω(x)/|x|n and[b,TΩ]be the commutator of TΩwith symbol b∈BMO(Rn).In this paper,the authors prove that if sup ζ∈Sn−1∫Sn−1|Ω(θ|logβ(1/|θ·ζ|)dθ2,then[b,TΩ]is bounded on Triebel–Lizorkin space F0,qp(Rn)provided that 1+1/β−1<p,q<β.
摘要This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).
摘要In this paper,we first introduce some new kinds of weighted amalgam spaces.Then we discuss the strong type and weak type estimates for a class of Calderόn-Zygmund type operators Tθin these new weighted spaces.Furthermore,the strong type estimate and endpoint estimate of linear commutators[b,Tθ]formed by b and Tθare established.Also we study related problems about two-weight,weak type inequalities for Tθand[b,Tθ]in the weighted amalgam spaces and give some results.
基金supported by NNSF of China(No.11271330)NNSF of Zhejiang(No.Y604563)PRSF ofZhejiang(No.BSH1302046)
摘要In this paper, we discuss the boundedness of commutators of high dimensional Hausdorff operator He on Herz type spaces. In addition, central BMO estimates for such commutators are also presented.
基金supported by NSF of Anhui Province(No.1608085QA12)NSF of Education Committee of Anhui Province(Nos.KJ2016A506 and KJ2017A454)+2 种基金Excellent Young Talents Foundation of Anhui Province(No.GXYQ2017070)Doctoral Scientific Research Foundation of Chaohu University(No.KYQD-201605)Scientific Research Project of Chaohu University(No.XLY-201501)
摘要In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO(μ) functions on non-homogeneous metric measure spaces is obtained.
基金Supported by the Natural Science Foundation of Zhejiang Province(Y6090359,Y6090383)Department of Education of Zhejiang Province(Z200803357)the NNSF of China(10701064)
摘要In this paper,the LP(Rn)-boundedness of the commutators generalized by BMO(Rn)function and the singular integral operator T with rough kernelΩ∈L log+L(Sn-1)is proved by using the Bony's formula for the paraproduct of two functions.
基金Supported by the National Natural Science Foundation of China(10571182)
摘要Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The L^P boundedness of the nested commutators is proved on product spaces, where 1<p<∞.
基金supported by National Natural Foundation of China (Grant Nos. 11161042 and 11071250)
摘要In this paper, by applying the technique of the sharp maximal function and the equivalent representation of the norm in the Lebesgue spaces with variable exponent, the boundedness of the parameterized Litflewood-Paley operators, including the parameterized Lusin area integrals and the parameterized Littlewood-Paley gλ^*- functions, is established on the Lebesgue spaces with variable exponent. Furthermore, the boundedness of their commutators generated respectively by BMO functions and Lipschitz functions are also obtained.
摘要In this paper,we introduce the weighted multilinear p-adic Hardy operator and weighted multilinear p-adic Ces`aro operator,we also obtain the boundedness of these two operators on the product of p-adic Herz spaces and p-adic Morrey-Herz spaces,the corresponding operator norms are also established in each case.Moreover,the boundedness of commutators of these two operators with symbols in central bounded mean oscillation spaces and Lipschitz spaces on p-adic Morrey-Herz spaces are also given.
基金supported by National Natural Science Foundation of China (10701078)supported by National Science Foundation for Distinguished Young Scholars (10425106)
摘要Let μ be a nonnegative Radon measure on Rd, which only satisfies the polynomial growth condition. Under this assumption, the authors obtain some weighted weaktype estimates for the commutators generated by the multilinear CalderSn-Zygmund op- erators and RBMO(μ) functions.
基金Supported by the National Natural Science Foundation of China (10771054, 10771221, 11071200)the Youth Foundation of Wuyi University (No. xq0930)
摘要This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department(09A058)
摘要Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained.The vector-valued case is also considered.