Dimitrios Betsakos, Christina Karafyllia, Nikolaos Karamanlis
Abstract
Abstract We prove that for $0 and $-1<\alpha <+\infty ,$ a conformal map defined on the unit disk belongs to the weighted Bergman space $A_{\alpha }^p$ if and only if a certain integral involving the hyperbolic distance converges.
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Abstract We prove that for $0 and $-1<\alpha <+\infty ,$ a conformal map defined on the unit disk belongs to the weighted Bergman space $A_{\alpha }^p$ if and only if a certain integral involving the hyperbolic distance converges.
Key concepts: Mathematics, Unit disk, Conformal map, Bergman space, Space (punctuation), Pure mathematics, Metric (unit), Mathematical analysis