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Real-variable characterizations of Bergman spaces

By Zeqian Chen and Wei Ouyang


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.Comment: 17 pages. a minor change made. arXiv admin note: text overlap with arXiv:1005.293

Topics: Mathematics - Functional Analysis, Mathematics - Complex Variables, 46E15, 32A36, 32A50
Year: 2011
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