The molecular characterization of the Hardy space H1 on non-homogeneous metric measure spaces and its application

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Fu, Xing¹  Yang, Dachun¹  Yang, Dongyong² 

[1] Beijing Normal Univ, Sch Math Sci, Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

关键词: Non-homogeneous metric measure space;    Hardy space;    Atom;    Molecule;    Calderon-Zygmund operator;    RBMO(mu);   

DOI  :  10.1016/j.jmaa.2013.09.021

来源: Elsevier

【 摘 要 】

Let (X, d, mu) be a non-homogeneous metric measure space, which means that (X, d, mu) is a metric measure space satisfying both the geometrically doubling and the upper doubling conditions. In this paper, the authors introduce the atomic Hardy space (H) over tilde (1,p)(atb)(mu) via the discrete coefficient (K) over tilde ((rho))(B,S) for p is an element of (1, infinity) and balls B subset of S of X. Then, the authors establish the corresponding molecular characterization of (H) over tilde (1,p)(atb)(mu) via a constructive way. As an application, the authors obtain the boundedness of Calderon-Zygmund operators on (H) over tilde (1,p)(atb)(mu). Moreover, the authors give a sufficient condition to guarantee that (H) over tilde (1,p)(atb)(mu) coincides with the existing atomic Hardy space H-atb(1,p)(mu). (C) 2013 Elsevier Inc. All rig1.4s reserved.

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