In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the c...In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.展开更多
Let X be a ball quasi-Banach function space on R^(n).In this article,we introduce the weak Hardytype space WH_(X)(R^(n)),associated with X,via the radial maximal function.Assuming that the powered HardyLittlewood maxi...Let X be a ball quasi-Banach function space on R^(n).In this article,we introduce the weak Hardytype space WH_(X)(R^(n)),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 WH_(X)(R^(n)),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 H_(X)(R^(n))to WH_(X)(Rn),which includes the critical case.All these results are of wide applications.Particularly,when X:=M^(q)_(p)(R^(n))(the Morrey space),X:=L^(p)(R^(n))(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
We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces,weighted weak Lebesgue spaces,weighted Hardy spaces and weighted weak Hardy spaces.The...We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces,weighted weak Lebesgue spaces,weighted Hardy spaces and weighted weak Hardy spaces.The sharpness of some results is also investigated.展开更多
Recently, J. Garcia-Cuerva, along with Y. Z. Chen and K. S. Lau, defined some Hardy spaces HA^p associated with the Beurling algebra A^p (1【p【∞)and gave their atomic decompositions. The main purpose of this note is...Recently, J. Garcia-Cuerva, along with Y. Z. Chen and K. S. Lau, defined some Hardy spaces HA^p associated with the Beurling algebra A^p (1【p【∞)and gave their atomic decompositions. The main purpose of this note is to find out the boundedness of Caldern-Zygmund operators on HA^p. As a corollary, we obtain a necessary condition of wavelet series in HA^p . By Lu’s constructive method in [3], we can generalize the above results to the weighted situation. For this purpose, let us begin with the weighted central atom.展开更多
It was well known that the maximal Fourier partial sums operator Sf=sup|S_nf| does not satisfy weak type (1, 1) inequality. However, Sf satisfies the following Taibleson-Weiss’s
This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the...This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the author establishes the boundedness on certain endpoint Triebel-Lizorkin spaces F˙10 ,q（2 q ≤ ∞） under a very weak pointwise regularity condition.展开更多
Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<s...Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<sup>n</sup>）×…×HK<sub>qk</sub><sup>αk,pk</sup>（R<sup>n</sup>）into HK<sub>q</sub><sup>α,p</sup>（R<sup>n</sup>）if they have vanishing moments up to a certain order dictated by the target spaces.These conditions on vanishing moments satisfied by the multilinear operators are also necessary when α<sub>j</sub>（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.展开更多
In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ<SUP> n </SUP>are introduced, and the central atomic and molecular decomposition characte...In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ<SUP> n </SUP>are introduced, and the central atomic and molecular decomposition characterizations of those spaces are established. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy spaces.展开更多
基金Supported by the Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities(ZZQ10010)Supported by the Fund for the Doctoral Program of Higher Education(20090141120010)
文摘In this paper, we introduce a class of non-convolution-type Calderón-Zygmund operators, whose kernels are certain sums involving the products of the Daubechies wavelets and their convolutions. And we obtain the continuity on the Besov spaces B 0,q p (1 ≤ p, q ≤∞), which is mainly dependent on the properties of the Daubechies wavelets and Lemari's T1 theorem for Besov spaces.
基金supported by National Natural Science Foundation of China(Grant Nos.11971058,11761131002,11671185 and 11871100)。
文摘Let X be a ball quasi-Banach function space on R^(n).In this article,we introduce the weak Hardytype space WH_(X)(R^(n)),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 WH_(X)(R^(n)),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 H_(X)(R^(n))to WH_(X)(Rn),which includes the critical case.All these results are of wide applications.Particularly,when X:=M^(q)_(p)(R^(n))(the Morrey space),X:=L^(p)(R^(n))(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.
基金Dachun Yang was partially supported by the NNSF and the SEDF of China
文摘We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces,weighted weak Lebesgue spaces,weighted Hardy spaces and weighted weak Hardy spaces.The sharpness of some results is also investigated.
基金Project supported by the National Natural Science Foundation of China.
文摘Recently, J. Garcia-Cuerva, along with Y. Z. Chen and K. S. Lau, defined some Hardy spaces HA^p associated with the Beurling algebra A^p (1【p【∞)and gave their atomic decompositions. The main purpose of this note is to find out the boundedness of Caldern-Zygmund operators on HA^p. As a corollary, we obtain a necessary condition of wavelet series in HA^p . By Lu’s constructive method in [3], we can generalize the above results to the weighted situation. For this purpose, let us begin with the weighted central atom.
基金Project supported by the National Natural Science Foundation of China.
文摘It was well known that the maximal Fourier partial sums operator Sf=sup|S_nf| does not satisfy weak type (1, 1) inequality. However, Sf satisfies the following Taibleson-Weiss’s
基金Supported by the National Natural Science Foundation of China (Grant No. 10871209)Research Fund for the Doctoral Program of Higher Education (Grant No. 20090141120010)
文摘This paper focuses on the study of the boundedness of convolution-type Calderón-Zygmund operators on some endpoint Triebel-Lizorkin spaces. Applying wavelets, molecular decomposition and interpolation theory, the author establishes the boundedness on certain endpoint Triebel-Lizorkin spaces F˙10 ,q（2 q ≤ ∞） under a very weak pointwise regularity condition.
基金The second author is partially supported by the NNSF and the SEDF of Chinathe Grant-in-Aid for Scientific Research (11304009),Japan Society for the Promotion of Science
文摘Let k ∈ N.We prove that the lnultilinear operators of finite sums of products of singular integrals on R<sup>n</sup> are bounded from H K<sub>ql</sub><sup>αl·pl</sup>（R<sup>n</sup>）×…×HK<sub>qk</sub><sup>αk,pk</sup>（R<sup>n</sup>）into HK<sub>q</sub><sup>α,p</sup>（R<sup>n</sup>）if they have vanishing moments up to a certain order dictated by the target spaces.These conditions on vanishing moments satisfied by the multilinear operators are also necessary when α<sub>j</sub>（?）0 and the singular integrals considered here include the Calderón-Zygmund singular integrals and the fractional integrals of any orders.
基金NSF of China (Grant Nos.10571014 and 10571015)SRFDP of China (Grant No.20050027025)
文摘In this paper, a class of anisotropic Herz-type Hardy spaces associated with a non-isotropic dilation on ℝ<SUP> n </SUP>are introduced, and the central atomic and molecular decomposition characterizations of those spaces are established. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of the central δ-Calderón-Zygmund operators on the anisotropic Herz-type Hardy spaces.
