区域上Besov空间的分子分解及其应用

数学物理学报 ›› 2013, Vol. 33 ›› Issue (5): 926-936.

区域上Besov空间的分子分解及其应用

赵凯¹|李澎涛^1,2

1.青岛大学数学科学学院山东青岛 266071;
2.汕头大学数学系广东汕头 515063

收稿日期:2012-01-10 修回日期:2013-06-12 出版日期:2013-10-25 发布日期:2013-10-25
基金资助:
国家自然科学基金(11041004)和山东省自然科学基金(ZR2010AM032)资助.

Molecular Decompositions of Besov Spaces on Domains and an Application

ZHAO Kai¹, LI Peng-Tao^1,2

1.College of Mathematics, Qingdao University, Shandong Qingdao 266071;
2.Department of Mathematics, Shantou University, Guangdong Shantou |515063

Received:2012-01-10 Revised:2013-06-12 Online:2013-10-25 Published:2013-10-25
Supported by:
国家自然科学基金(11041004)和山东省自然科学基金(ZR2010AM032)资助.

摘要/Abstract

摘要：

基于区域上Besov空间的原子, 引进了分子的概念. 利用区域上Calder\'{o}n型表示定理, 得到了区域上更宽泛的Besov空间的分子分解. 作为应用, 证明了Calder\'{o}n-Zygmund算子在这类Besov空间上的有界性.

关键词: Besov空间, 区域, 分子分解, Calderon-Zygmund算子

Abstract:

Based on the atoms of Besov spaces defined on domains, the molecules are introduced. By using the Calder\'{o}n type reproducing formula on domains, the molecular decompositions of a wider range of Besov spaces on domains are obtained. As an application, it is proved that the Calder\'{o}n-Zygmund operators are bounded on such Besov spaces.

Key words: Besov space, Domain, Molecular decomposition, Calderon-Zygmund operator

中图分类号:

42B35

赵凯, 李澎涛. 区域上Besov空间的分子分解及其应用[J]. 数学物理学报, 2013, 33(5): 926-936.

ZHAO Kai, LI Peng-Tao. Molecular Decompositions of Besov Spaces on Domains and an Application[J]. Acta mathematica scientia,Series A, 2013, 33(5): 926-936.

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