Molecular Characterization of Anisotropic Musielak–Orlicz Hardy Spaces and Their Applications  

作　　者：Bao De LI Xing Ya FAN Zun Wei FU Da Chun YANG 

机构地区：[1]College of Mathematics and System Science,Xinjiang University [2]Department of Mathematics,Linyi University [3]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education

出　　处：《Acta Mathematica Sinica,English Series》2016年第11期1391-1414,共24页数学学报（英文版）

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);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)

摘　　要：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.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.

关 键 词：Anisotropic expansive dilation Muckenhoupt weight Musielak–Orlicz function Hardy space MOLECULE anisotropic Calderón–Zygmund operator 

分 类 号：O177[理学—数学]