In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey ...In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.展开更多
In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding ...In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular CalderSn- Zygmund operators and weighted Lipschitz functions can also be obtained.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
Let A be an expansive dilation on Rn and φ ： Hn×[0, ∞）→[0, ∞） an anisotropic Musielak-Orlicz function. Let HAφ（R^n） be the anisotropic Hardy space of Musielak-Orlicz type defined via the grand maximal f...Let A be an expansive dilation on Rn and φ ： Hn×[0, ∞）→[0, ∞） an anisotropic Musielak-Orlicz function. Let HAφ（R^n） be the anisotropic Hardy space of Musielak-Orlicz type defined via the grand maximal function. In this article, the authors establish its molecular characterization via the atomic characterization of HAφ（R^n）. The molecules introduced in this article have the vanishing moments up to order s and the range of s in the isotropic case （namely, A ：= 2In×n） coincides with the range of well-known classical molecules and, moreover, even for the isotropic Hardy space HP（R^n） with p∈[（0, 1] （in this case, A ：= 2In×n,φ（x, t） ：= t^p for all x ∈ R^n and t∈[0,∞））, this molecular characterization is also new. As an application, the authors obtain the boundedness of anisotropic Caldeon-Zygmund operators from HA^φ（Hn） to L^φ（R^n） or from HA^φ（Hn） to itself.展开更多
In this paper, we give a complete real-variable theory of local variable Hardy spaces.First, we present various real-variable characterization in terms of several local maximal functions.Next, the new atomic and the f...In this paper, we give a complete real-variable theory of local variable Hardy spaces.First, we present various real-variable characterization in terms of several local maximal functions.Next, the new atomic and the finite atomic decomposition for the local variable Hardy spaces are established. As an application, we also introduce the local variable Campanato space which is showed to be the dual space of the local variable Hardy spaces. Analogous to the homogeneous case, some equivalent definitions of the dual of local variable Hardy spaces are also considered. Finally, we show the boundedness of inhomogeneous Calderon–Zygmund singular integrals and local fractional integrals on local variable Hardy spaces and their duals.展开更多
基金Supported by the National Natural Science Foundation of China(10571014)the Doctoral Programme Foundation of Institution of Higher Education of China(20040027001)
文摘In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.
基金Supported by National Natural Science Foundation of China(Grant No.11171345)the Fundamental Research Funds for the Central Universities(Grant No.2009QS16)the State Scholarship Fund of China
文摘In this paper, the authors establish the boundedness of commutators generated by strongly singular CalderSn-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular CalderSn- Zygmund operators and weighted Lipschitz functions can also be obtained.
文摘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partially supported by National Natural Science Foundation of China(Grant Nos.11461065,11161044,11571039 and 11361020)supported by Scientific Research Projects in Colleges and Universities in Xinjiang Uyghur Autonomous Region(Grant No.XJEDU2014S001)+2 种基金supported by National Natural Science Foundation of China(Grant No.11271175)partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2013YB60and 2014KJJCA10)
文摘Let A be an expansive dilation on Rn and φ ： Hn×[0, ∞）→[0, ∞） an anisotropic Musielak-Orlicz function. Let HAφ（R^n） be the anisotropic Hardy space of Musielak-Orlicz type defined via the grand maximal function. In this article, the authors establish its molecular characterization via the atomic characterization of HAφ（R^n）. The molecules introduced in this article have the vanishing moments up to order s and the range of s in the isotropic case （namely, A ：= 2In×n） coincides with the range of well-known classical molecules and, moreover, even for the isotropic Hardy space HP（R^n） with p∈[（0, 1] （in this case, A ：= 2In×n,φ（x, t） ：= t^p for all x ∈ R^n and t∈[0,∞））, this molecular characterization is also new. As an application, the authors obtain the boundedness of anisotropic Caldeon-Zygmund operators from HA^φ（Hn） to L^φ（R^n） or from HA^φ（Hn） to itself.
基金Supported by National Natural Science Foundation of China (Grant No. 11901309)Natural Science Foundation of Jiangsu Province of China (Grant No. BK20180734)+1 种基金Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 18KJB110022)Natural Science Foundation of Nanjing University of Posts and Telecommunications (Grant Nos. NY222168, NY219114)。
文摘In this paper, we give a complete real-variable theory of local variable Hardy spaces.First, we present various real-variable characterization in terms of several local maximal functions.Next, the new atomic and the finite atomic decomposition for the local variable Hardy spaces are established. As an application, we also introduce the local variable Campanato space which is showed to be the dual space of the local variable Hardy spaces. Analogous to the homogeneous case, some equivalent definitions of the dual of local variable Hardy spaces are also considered. Finally, we show the boundedness of inhomogeneous Calderon–Zygmund singular integrals and local fractional integrals on local variable Hardy spaces and their duals.
