Hyperbolic metric and membership of conformal maps in the Bergman space

2020/05/06 by Dimitrios Betsakos, Christina Karafyllia, Nikolaos Karamanlis · 2 citations
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Algebraic and Geometric Analysis

paper · doi:10.4153/s000843952000034x

Abstract

Abstract We prove that for 0<p<+∞ and -1<α <+∞ , a conformal map defined on the unit disk belongs to the weighted Bergman space A_α ^p if and only if a certain integral involving the hyperbolic distance converges.

Citations

• Composition operators between Bergman and Hardy spaces

Cited by

• Geometric characterizations for conformal mappings in weighted Bergman spaces
• On the Bergman number of hyperbolic domains

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