Lipschitz Type Characterizations for Bergman Spaces
نویسندگان
چکیده
منابع مشابه
Lipschitz Type Characterizations for Bergman Spaces
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.
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Let D be the open unit disk in the complex plane C. Denote by H(D) the class of all functions analytic on D. An analytic self-map φ : D → D induces the composition operator Cφ on H(D), defined by Cφ ( f ) = f (φ(z)) for f analytic on D. It is a well-known consequence of Littlewood’s subordination principle that the composition operator Cφ is bounded on the classical Hardy and Bergman spaces (se...
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ژورنال
عنوان ژورنال: Canadian Mathematical Bulletin
سال: 2009
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-2009-060-6