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
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.
