Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Yuan, Wen¹  Sawano, Yoshihiro²  Yang, Dachun¹ 

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

[2] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

关键词: phi-transform;    Hausdorff capacity;    Besov space;    Triebel-Lizorkin space;    Embedding;    Atom;    Molecule;    Trace;    Pseudo-differential operator;   

DOI  :  10.1016/j.jmaa.2010.04.021

来源: Elsevier

【 摘 要 】

Let p is an element of (1, infinity), q is an element of [1, infinity), s is an element of R and tau is an element of [0, 1 - 1/max{p,q}]. In this paper, the authors establish the phi-transform characterizations of Besov-Hausdorff spaces B(H) over dot(p,q)(s,t)(R-n) and Triebel-Lizorkin-Hausdorff spaces F(H) over dot(p,q)(s,t)(R-n) (q > 1); as applications, the authors then establish their embedding properties (which on B(H) over dot(p,q)(s,t)(R-n) is also sharp), smooth atomic and molecular decomposition characterizations for suitable tau. Moreover, using their atomic and molecular decomposition characterizations, the authors investigate the trace properties and the boundedness of pseudo-differential operators with homogeneous symbols in B(H) over dot(p,q)(s,t)(R-n) and F(H) over dot(p,q)(s,t)(R-n) (q > 1), which generalize the corresponding classical results on homogeneous Besov and Triebel-Lizorkin spaces when p is an element of (1, infinity) and q is an element of [1, infinity) by taking tau = 0. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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