We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish...We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.展开更多
Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of ...Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.展开更多
In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator...In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the into itself, if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable, i.e. satisfies the Matkowski’s weak condition.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.
The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this t...The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.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 article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable expo...In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.展开更多
In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.
In the case of Ω∈ Lipγ（S^n-1） （0 〈 γ ≤ 1）, we prove the boundedness of the Marcinkiewicz integral operator μΩ on the variable exponent Herz-Morrey spaces. Also, we prove the boundedness of the higher order...In the case of Ω∈ Lipγ（S^n-1） （0 〈 γ ≤ 1）, we prove the boundedness of the Marcinkiewicz integral operator μΩ on the variable exponent Herz-Morrey spaces. Also, we prove the boundedness of the higher order commutators μΩ^m,b with b ∈ BMO（R^n） on both variable exponent Herz spaces and Herz-Morrey spaces, and extend some known results.展开更多
In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey ...In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extend some known results.展开更多
In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） an...In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.展开更多
Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
In this paper, we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from Lp1 （＇） （Rn） to Lp2（） （Rn）.
In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents . By using the properties of the variable exponents Lebesgue spaces, the boun...In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents . By using the properties of the variable exponents Lebesgue spaces, the boundedness of the fractional integral operator and their commutator generated by Lipschitz function is obtained on those Herz spaces.展开更多
The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose,we first charact...The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose,we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators.Immediately after,applying the characterizations of TriebelLizorkin space with variable exponent,we obtain that b∈∧βif and only if the commutator of Calderon-Zygmund singular integral operator is bounded,respectively,from L^p(·)(R^n)toF^β,∞p(·),fromL^p(·)(R^n)toL^q(·)(R^n)with1/p(·)-1/q(·)=β/n.Moreover,we prove that the commutator of Riesz potential operator also has corresponding results.展开更多
Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.
In this paper, we study the boundedness of the fractional integral with variable kernel. Under some assumptions, we prove that such kind of operators is bounded from the variable exponent Herz-Morrey spaces to the var...In this paper, we study the boundedness of the fractional integral with variable kernel. Under some assumptions, we prove that such kind of operators is bounded from the variable exponent Herz-Morrey spaces to the variable exponent Herz-Morrey spaces.展开更多
In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mappi...In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicated estimate.展开更多
Let Ω ∈ L^2（S^n-1） be homogeneous function of degree zero and b be BMO functions. In this paper, we obtain some boundedness of the Littlewood-Paley Opera- tors and their higher-order commutators on Herz spaces wit...Let Ω ∈ L^2（S^n-1） be homogeneous function of degree zero and b be BMO functions. In this paper, we obtain some boundedness of the Littlewood-Paley Opera- tors and their higher-order commutators on Herz spaces with variable exponent.展开更多
基金Supported by the Natural Science Research Project of Anhui Educational Committee(Grant No.2024AH050129)。
文摘We prove the boundedness of the parametric Lusin's S functionμ_(S)^(?)(f)and Littlewood-Paley's g_(λ)^(*)-funtionμ_(λ),^(*,?)(f)on grand Herz-Morrey spaces with variable exponents.Additionally,we establish the boundedness of higher-order commutators ofμ_(S)^(?)andμ_(λ),^(*,?)with BMO functions applying some properties of variable exponents and generalized BMO norms.
文摘Wiener amalgam spaces are a class of function spaces where the function’s local and global behavior can be easily distinguished. These spaces are ex-tensively used in Harmonic analysis that originated in the work of Wiener. In this paper: we first introduce a two-variable exponent amalgam space (L<sup>q</sup><sup>()</sup>,l<sup>p</sup><sup>()</sup>)(Ω). Secondly, we investigate some basic properties of these spaces, and finally, we study their dual.
文摘In this paper we present the notion of the space of bounded p(·)-variation in the sense of Wiener-Korenblum with variable exponent. We prove some properties of this space and we show that the composition operator H, associated with , maps the into itself, if and only if h is locally Lipschitz. Also, we prove that if the composition operator generated by maps this space into itself and is uniformly bounded, then the regularization of h is affine in the second variable, i.e. satisfies the Matkowski’s weak condition.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘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Supported by the National Natural Science Foundation of China (11071065, 10771110, 10471069)sponsored by the 151 Talent Fund of Zhejiang Province
文摘The boundedness of multilinear singular integrals of Calder′on-Zygmund type onproduct of variable exponent Lebesgue spaces over both bounded and unbounded domains areobtained. Further more, the boundedness for this type multilinear operators on product ofvariable exponent Morrey spaces over domains is shown in the paper.
基金supported by National Natural Foundation of China (Grant Nos. 11161042 and 11071250)
文摘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.
基金supported by NSFC(11471251)supported by NSFC(11271293)
文摘In this article, by extending classical Dellacherie＇s theorem on stochastic se- quences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis in- equality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier＇s inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.
基金supported by NSFC (No. 11201003)University NSR Project of Anhui Province (No. KJ2014A087)
文摘In this paper, we prove the boundedness of the fractional maximal operator, Hardy-Littlewood maximal operator and marcinkiewicz integrals associated with Schrodinger operator on Morrey spaces with variable exponent.
基金Supported by the National Natural Science Foundation of China(Grant No.11201003)the Natural Science Foundation of Anhui Higher Education Institutions(Grant Nos.KJ2011A138KJ2013B034)
文摘In the case of Ω∈ Lipγ（S^n-1） （0 〈 γ ≤ 1）, we prove the boundedness of the Marcinkiewicz integral operator μΩ on the variable exponent Herz-Morrey spaces. Also, we prove the boundedness of the higher order commutators μΩ^m,b with b ∈ BMO（R^n） on both variable exponent Herz spaces and Herz-Morrey spaces, and extend some known results.
文摘In this paper, under natural regularity assumptions on the exponent function, we prove some boundedness results for the functions of Littlewood-Paley, Lusin and Marcinkiewicz on a new class of generalized Herz-Morrey spaces with weight and variable exponent, which essentially extend some known results.
基金supported by NSFC (No. 11201003)Education Committee of Anhui Province (No. KJ2012A133)
文摘In this paper, we will prove the boundedness of Hardy type operators Hβ（x） and Hβ^＊（x） of variable order β（x） on Herz spaces Kp（·）^α（·）q and Kp（·）^α（·）q′,where α（·） and p（·）are both variable.
基金supported by NSFC (No. 11101001 and No. 11201003)Education Committee of Anhui Province (No. KJ2011A138 and No. KJ2012A133)
文摘Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
基金Supported by the NSF of Zhejiang Province (Y6090681)the Education Dept.of Zhejiang Province(Y201120509)
文摘In this paper, we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from Lp1 （＇） （Rn） to Lp2（） （Rn）.
文摘In this paper, we study the boundedness of the fractional integral operator and their commutator on Herz spaecs with two variable exponents . By using the properties of the variable exponents Lebesgue spaces, the boundedness of the fractional integral operator and their commutator generated by Lipschitz function is obtained on those Herz spaces.
基金Supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant Nos.2019D01C334,2016D01C381)the National Natural Science Foundation of China(Grant No.11661075)。
文摘The main purpose of this paper is to characterize the Lipschitz space by the boundedness of commutators on Lebesgue spaces and Triebel-Lizorkin spaces with variable exponent.Based on this main purpose,we first characterize the Triebel-Lizorkin spaces with variable exponent by two families of operators.Immediately after,applying the characterizations of TriebelLizorkin space with variable exponent,we obtain that b∈∧βif and only if the commutator of Calderon-Zygmund singular integral operator is bounded,respectively,from L^p(·)(R^n)toF^β,∞p(·),fromL^p(·)(R^n)toL^q(·)(R^n)with1/p(·)-1/q(·)=β/n.Moreover,we prove that the commutator of Riesz potential operator also has corresponding results.
文摘Our aim in this paper is to prove the boundedness of commutators of Calderón-Zygmund operator with the Lipschitz function or BOM function on Herz-type Hardy space with variable exponent.
文摘In this paper, we study the boundedness of the fractional integral with variable kernel. Under some assumptions, we prove that such kind of operators is bounded from the variable exponent Herz-Morrey spaces to the variable exponent Herz-Morrey spaces.
文摘In this paper, we study a nonlinear parabolic system with variable exponents. The existence of classical solutions to an initial and boundary value problem is obtained by a fixed point theorem of the contraction mapping, and the blow-up property of solutions in finite time is obtained with the help of the eigenfunction of the Laplace equation and a delicated estimate.
文摘Let Ω ∈ L^2（S^n-1） be homogeneous function of degree zero and b be BMO functions. In this paper, we obtain some boundedness of the Littlewood-Paley Opera- tors and their higher-order commutators on Herz spaces with variable exponent.
