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Lipschitz Type Characterizations for Bergman Spaces

Published online by Cambridge University Press:  20 November 2018

Hasi Wulan  and
Kehe Zhu
Hasi Wulan
Affiliation:
Department of Mathematics, Shantou University, Guangdong, China e-mail: wulan@stu.edu.cn
Kehe Zhu
Affiliation:
Department of Mathematics, SUNY, Albany, NY 12222, USA e-mail: kzhu@math.albany.edu
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Abstract

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We obtain new characterizations for Bergman spaces with standard weights in terms of Lipschitz type conditions in the Euclidean, hyperbolic, and pseudo-hyperbolic metrics. As a consequence, we prove optimal embedding theorems when an analytic function on the unit disk is symmetrically lifted to the bidisk.

Keywords

32A36Bergman spaceshyperbolic metricLipschitz condition
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 4 , 01 December 2009 , pp. 613 - 626
Copyright
Copyright © Canadian Mathematical Society 2009

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