紧致齐性空间上的调和分析——H^p空间的分子分解

Harmonic Analysis on the Compact Homogeneous Spaces-Molecular Theory of H^p-Space

本文研究紧齐性空间M上的H^p(M)空间的分子理论及其在算子有界性问题中应用,主要证明了关于H^p(M)空间具有分子分解结构的定理。

In this paper, we study molecular theory of Hp-space on the Compact homogeneous space, we proved mainly theThorein 3. If f∈s' , then f 6Hap,q (M), if and only if f can be expressed as , where every Mk is a (p,q,s) molecular or exceptionalmolecular, is irrelevant to k), andTherein 4. If for every (p,q,s) atom or exceptional atom a, Ta is a (p,q,s,ε) molecular or exceptional molecular, and nq(Ta)≤c, (c is irrelevant to a), then T is type of (Hp Hp)