Bergman空间的实变刻画(英文)

Real-variable Characterizations of Bergman Spaces

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.