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arXiv · 1104.3960

Real-variable characterizations of Bergman spaces

Zeqian Chen·Wei Ouyang
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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.

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Zeqian Chen, Wei Ouyang. 2011-04-20. Real-variable characterizations of Bergman spaces. https://arxiv.org/abs/1104.3960

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