Bergman空间的实变刻画(英文)  

Real-variable Characterizations of Bergman Spaces

作　　者：陈泽乾[1] 欧阳威[1,2] 

机构地区：[1]中国科学院武汉物理与数学研究所,武汉430071 [2]中国科学院研究生院,北京100049

出　　处：《应用泛函分析学报》2011年第3期246-259,共14页Acta Analysis Functionalis Applicata

摘　　要：介绍复球上Bergman空间实变理论的某些新进展,包括Bergman空间关于Carleson矩形的实变原子分解,极大函数和面积函数刻画以及运用帐篷空间的实变刻画.特别是,用齐次空间上向量值Calderon-Zygmund奇异积分算子理论研究Bergman积分算子的L^p有界性并给出了Bergman空间面积积分刻画的新证明.In this paper, we give a survey of results obtained recently by the present authors on real-variable characterizations of Bergman spaces, which are closely related to maximal and area integral functions in terms of the Bergman metric. In particular, we give a new proof of those results concerning area integral characterizations through using the method of vector-valued Calderdn- Zygmund operators to handle Bergman singular integral operators on the complex bail. The proofs involve some sharp estimates of the Bergman kernel function and Bergman metric.

关 键 词：BERGMAN空间 Bergman距离 极大函数 面积函数 Bergman积分算子 

分 类 号：O177.2[理学—数学]