Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2...Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2)whenγ=nβ/2,α=n(1-1/q).Also,for the unweighted case,we obtain the Hk_(q)^(α,p)(R^(n))boundedness of Tγ,βunder certain conditions on y.These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun.As an application,we prove the HK_(q)^(α,p)(R^(n))boundedness of the spherical average S_(t)^(δ)uniformly on t>0.展开更多
In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-...In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers.展开更多
In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.
This paper establishes some strong type and weak type estimates for commutator [b,I1] on Herz-type spaces, where b E BMO(Rn) and I1 is a fractional integration with O < l < n.
In this paper, the boundedness of mulitilinear commutator [-b,T] on Herz-type space is considered, where T is a standard Calderon-Zygmund singular operator and -b ∈ （BMO（Rn））m.
Let (.the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces (w2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces,...Let (.the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces (w2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show that , the class of C(Rn)-functions with compactly support, is dense in and there is a subsequence, which converges in distrbutional sense to some distribution of , of any bounded sequence in In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.展开更多
In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.
In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from HKq^a、P（ω1;ω2） into Kq^a、p （ω1; ω2）.
In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional ope...In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.展开更多
In this paper,the authors first establish some new real-variable characterizations of Herz- type Hardy spaces H<sub>q</sub><sup>α,p</sup>（ω<sub>1</sub>;ω<sub>2</sub>...In this paper,the authors first establish some new real-variable characterizations of Herz- type Hardy spaces H<sub>q</sub><sup>α,p</sup>（ω<sub>1</sub>;ω<sub>2</sub>）and HK<sub>q</sub><sup>α,P</sup>（ω<sub>1</sub>;ω<sub>2</sub>）,where ω<sub>1</sub>,ω<sub>2</sub> ∈A<sub>1</sub>-weight,1【q【∞, n（1-1/q）≤α【∞ and 0【p【∞.Then,using these new characterizations,they investigate the convergence of a bounded set in these spaces,and study the boundedness of some potential operators on these spaces.展开更多
Basic properties of the Herz-type Hardy spaces HK<sub>q</sub><sup>a,p</sup>, such as the boundedness of singular integral operators and the fractional integration operators, atomic decompositio...Basic properties of the Herz-type Hardy spaces HK<sub>q</sub><sup>a,p</sup>, such as the boundedness of singular integral operators and the fractional integration operators, atomic decomposition, dense subspaces, etc., are established in the full range 0【q【∞.展开更多
Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Har...Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section.展开更多
We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multipl...We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.展开更多
In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2...In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2（｜x｜^t; ｜x｜^t） and HK^α,P 2（｜x｜^t; ｜x｜^t）.展开更多
In this paper,we mainly investigate the boundedness of Littlewood-Paley functions and pseudo-differential operators on weighted Herz-type Hardy spaces over locally compact Vilenkin groups.
Soria and Weiss extended a Stein’s result,the boundedness of singular integral op-erators on the weighted spaces L^p(w) with power weights w, to more general cases wheresingular integral operators were replaced by su...Soria and Weiss extended a Stein’s result,the boundedness of singular integral op-erators on the weighted spaces L^p(w) with power weights w, to more general cases wheresingular integral operators were replaced by sublinear operators T satisfying the size condi-tion (for compact supported function f)展开更多
基金supported by the National Key Research and Development Program of China(22YFA10057001)the National Science Foundation of Guangdong Province(2023A1515012034)the National Natural Science Foundation of China(12371105,11971295).
文摘Let 0<p≤1<q<∞,andω1,ω2 E A1(Muckenhoupt-class).We study an oscillating multiplier operator Tγ,βand obtain that it is boundedon the homogeneous weighted Herz-type Hardy spaces HK_(q)^(α,p)(R^(n);ω1,ω2)whenγ=nβ/2,α=n(1-1/q).Also,for the unweighted case,we obtain the Hk_(q)^(α,p)(R^(n))boundedness of Tγ,βunder certain conditions on y.These results are substantial improvements and extensions of the main results in the papers by Li and Lu and by Cao and Sun.As an application,we prove the HK_(q)^(α,p)(R^(n))boundedness of the spherical average S_(t)^(δ)uniformly on t>0.
基金Xu Jingshi was partially supported by NSF of Hunan in ChinaYang DaChun was partially supported by NNSF(10271015)and SEDF of China
文摘In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers.
文摘In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.
文摘This paper establishes some strong type and weak type estimates for commutator [b,I1] on Herz-type spaces, where b E BMO(Rn) and I1 is a fractional integration with O < l < n.
基金Supported by the National Natural Science Foundation of China(10771054, 10861010)the Scientific Re-search Program of Institutions of Higher Education of XinJiang(2008S58)the Natural Science Fund of Xinjiang University(YX080106, BS090101)
文摘In this paper, the boundedness of mulitilinear commutator [-b,T] on Herz-type space is considered, where T is a standard Calderon-Zygmund singular operator and -b ∈ （BMO（Rn））m.
基金Supported by the NECF and the NECF and the NNSF of China
文摘Let (.the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces (w2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish the boundedness on these spaces of the pseudo-differential operators of order zero and show that , the class of C(Rn)-functions with compactly support, is dense in and there is a subsequence, which converges in distrbutional sense to some distribution of , of any bounded sequence in In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
基金Supported by the NSF of China (10371087)NSF of Anhui Province (07021019)+2 种基金Education Committee ofAnhui Province (KJ2007A009Kj2008B244)the Grant for Younth of Anhui Normal University (2009xqn58)
文摘In this paper, we study the boundedness of higher order commutators of gen- eralized fractional integral operators on weighted Lp spaces and Herz-type Hardy spaces.
文摘In this paper, we discuss the boundedness of Marcinkiewicz integral μΩ with homogeneous kernel on the weighted Herz-type Hardy spaces, and prove that μΩ is bounded from HKq^a、P（ω1;ω2） into Kq^a、p （ω1; ω2）.
文摘In this paper, the authors study the multilinear operators with Dini Kernel and obtain their boundedness from Herz spaces to Herz-type Hardy spaces. Moreover, the authors also consider the corresponding fractional operators.
基金Partially by National Natural Science Foundation Funds （10701010）, Key University Science Research Project of Anhui Province （KJ2011A138） and Ph. D. Science Research Fund of Anhui Normal University.
文摘In this paper,the authors first establish some new real-variable characterizations of Herz- type Hardy spaces H<sub>q</sub><sup>α,p</sup>（ω<sub>1</sub>;ω<sub>2</sub>）and HK<sub>q</sub><sup>α,P</sup>（ω<sub>1</sub>;ω<sub>2</sub>）,where ω<sub>1</sub>,ω<sub>2</sub> ∈A<sub>1</sub>-weight,1【q【∞, n（1-1/q）≤α【∞ and 0【p【∞.Then,using these new characterizations,they investigate the convergence of a bounded set in these spaces,and study the boundedness of some potential operators on these spaces.
基金Partly supported by the Grants-in-Aid for Scientific Research (A)(1) 11304009, (B)(1)10440046, Japan Society for the Promotion of Science.
文摘Basic properties of the Herz-type Hardy spaces HK<sub>q</sub><sup>a,p</sup>, such as the boundedness of singular integral operators and the fractional integration operators, atomic decomposition, dense subspaces, etc., are established in the full range 0【q【∞.
文摘Let G be a locally compact Vilenkin group. In this paper the authors study the boundedness of bilinear operators B（f, g） given by finite sums of products of Calderdn-Zygmund operators in Herz space and Herz-type Hardy space on G. And an example, the boundedness from the products of Herz space to Herz-type Hardy space is given in the last section.
基金supported by Key Academic Discipline of Zhejiang Province of China and National NaturalScience Foundation of China (Grant Nos. 10571014, 10631080, 10671019)
文摘We establish Jackson-type and Bernstein-type inequalities for multipliers on Herz-type Hardy spaces. These inequalities can be applied to some important operators in Fourier analysis, such as the Bochner-Riesz multiplier over the critical index, the generalized Bochner-Riesz mean and the generalized Able-Poisson operator.
基金Research is supported in part by National Science Council in Taipei
文摘In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2（｜x｜^t; ｜x｜^t） and HK^α,P 2（｜x｜^t; ｜x｜^t）.
文摘In this paper,we mainly investigate the boundedness of Littlewood-Paley functions and pseudo-differential operators on weighted Herz-type Hardy spaces over locally compact Vilenkin groups.
文摘Soria and Weiss extended a Stein’s result,the boundedness of singular integral op-erators on the weighted spaces L^p(w) with power weights w, to more general cases wheresingular integral operators were replaced by sublinear operators T satisfying the size condi-tion (for compact supported function f)
