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

作者：Li, Bao De; Fan, Xing Ya; Fu, Zun Wei; Yang, Da Chun^*

来源：Acta Mathematica Sinica-English Series, 2016, 32(11): 1391-1414.

DOI：10.1007/s10114-016-4741-y

• Anisotropic expansive dilation
• Muckenhoupt weight
• Musielak-Orlicz function
• Hardy space
• molecule
• anisotropic Calderon-Zygmund operator

Let A be an expansive dilation on R-n and phi : R-n x [0, infinity) -> [0, infinity) an anisotropic Musielak-Orlicz function. Let H-A(phi)(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 H-A(phi)(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 := 2I(nxn)) coincides with the range of well-known classical molecules and, moreover, even for the isotropic Hardy space H-p(R-n) with p is an element of(0, 1] (in this case, A := 2I(nxn), phi(x, t) := t(p) for all x is an element of R-n and t is an element of[0, infinity)), this molecular characterization is also new. As an application, the authors obtain the boundedness of anisotropic Calderon-Zygmund operators from H-A(phi)(R-n) to L-phi (R-n) or from H-A(phi)(R-n) to itself.

• 出版日期2016-11
• 单位临沂大学; 新疆大学; 北京师范大学