We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their b...We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.展开更多
We prove the boundedness of the maximal operator Mr in the spaces L^p（·）（Г,p） with variable exponent p（t） and power weight p on an arbitrary Carleson curve under the assumption that p（t） satisfies the lo...We prove the boundedness of the maximal operator Mr in the spaces L^p（·）（Г,p） with variable exponent p（t） and power weight p on an arbitrary Carleson curve under the assumption that p（t） satisfies the log-condition on Г. We prove also weighted Sobolev type L^p（·）（Г, p） → L^q（·）（Г, p）-theorem for potential operators on Carleson curves.展开更多
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali...Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.展开更多
Let G be a homogeneous group. In this paper, the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G. As its special case, the corresponding result of multilinea...Let G be a homogeneous group. In this paper, the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G. As its special case, the corresponding result of multilinear Calderon-Zygmund operators can be obtained.展开更多
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 T_(λτc,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 T_(λτc,k,k′)from L^(p)(B_(n),dv_(α))to L^(q)(B_(n),dv_(β))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
Let G be a locally compact Abelian group with Haar measure.The authors discuss some basic properties of L_(w_1)~r(G) ∩ L(p,q,w_2dμ)(G) spaces.Then the necessary conditions for compact embeddings of the spaces L_(w_1...Let G be a locally compact Abelian group with Haar measure.The authors discuss some basic properties of L_(w_1)~r(G) ∩ L(p,q,w_2dμ)(G) spaces.Then the necessary conditions for compact embeddings of the spaces L_(w_1)~r(R^d)∩L(p,q,w_2dμ)(R^d) are showed.展开更多
We obtain the operator norms of the n-dimensional fractional Hardy operator Hα（0 〈 α 〈 n） from weighted Lebesgue spaces Lp｜x｜p（R^n） to weighted weak Lebesgue spacesLq,∞｜x｜β（R^n）.
In this paper,we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups,involving weighted Lebesgue spaces,classical Morrey spaces and central Morrey spaces.Meanwhile,s...In this paper,we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups,involving weighted Lebesgue spaces,classical Morrey spaces and central Morrey spaces.Meanwhile,some necessary and sufficient conditions of boundness are obtained.展开更多
This article is devoted to study the existence of renormalized solutions for the nonlinear p （x）-parabolic problem in the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity cond...This article is devoted to study the existence of renormalized solutions for the nonlinear p （x）-parabolic problem in the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity condition.展开更多
基金Both authors are supported in part by the Azerbaijan-U.S. Bilateral Grants Program (project ANSF Award / 3102)The second author is also supported in part by NSF grant, DMS 0200587
文摘We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.
文摘We prove the boundedness of the maximal operator Mr in the spaces L^p（·）（Г,p） with variable exponent p（t） and power weight p on an arbitrary Carleson curve under the assumption that p（t） satisfies the log-condition on Г. We prove also weighted Sobolev type L^p（·）（Г, p） → L^q（·）（Г, p）-theorem for potential operators on Carleson curves.
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012429)Guangzhou Huashang College Research Team Project(Grant No.2021HSKT03)。
文摘Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.
基金The NNSF(10571014)of Chinathe Doctoral Programme Foundation(20040027001)of Institution of Higher Education of China
文摘Let G be a homogeneous group. In this paper, the author studies the boundedness of multi-sublinear operators on the product of weighted Lebesgue spaces on G. As its special case, the corresponding result of multilinear Calderon-Zygmund operators can be obtained.
基金supported by the Education Department Important Foundation of Hunan Province in China(23A0095).
文摘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 T_(λτc,k,k′)from L^(p)(B_(n),dv_(α))to L^(q)(B_(n),dv_(β))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).
文摘Let G be a locally compact Abelian group with Haar measure.The authors discuss some basic properties of L_(w_1)~r(G) ∩ L(p,q,w_2dμ)(G) spaces.Then the necessary conditions for compact embeddings of the spaces L_(w_1)~r(R^d)∩L(p,q,w_2dμ)(R^d) are showed.
基金supported by National Natural Science Foundation of China(Grant Nos.11471040 and 11761131002).
文摘In this paper,we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups,involving weighted Lebesgue spaces,classical Morrey spaces and central Morrey spaces.Meanwhile,some necessary and sufficient conditions of boundness are obtained.
文摘This article is devoted to study the existence of renormalized solutions for the nonlinear p （x）-parabolic problem in the Weighted-Variable-Exponent Sobolev spaces, without the sign condition and the coercivity condition.
