English

Real-variable characterizations of Bergman spaces

Functional Analysis 2013-08-22 v2 Complex Variables

Abstract

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 Calder\'{o}n-Zygmund operators to handle Bergman singular integral operators on the complex ball. The proofs involve some sharp estimates of the Bergman kernel function and Bergman metric.

Keywords

Cite

@article{arxiv.1104.3960,
  title  = {Real-variable characterizations of Bergman spaces},
  author = {Zeqian Chen and Wei Ouyang},
  journal= {arXiv preprint arXiv:1104.3960},
  year   = {2013}
}

Comments

17 pages. a minor change made. arXiv admin note: text overlap with arXiv:1005.2936

R2 v1 2026-06-21T17:56:40.525Z