Geodesic
Hyperbolic metric and membership of conformal maps in the Bergman space
Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 174-181

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DOI

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.
DOI : 10.4153/S000843952000034X
Mots-clés : Bergman space, hyperbolic distance, Green function, conformal mapping 
Betsakos, Dimitrios; Karafyllia, Christina; Karamanlis, Nikolaos. Hyperbolic metric and membership of conformal maps in the Bergman space. Canadian mathematical bulletin, Tome 64 (2021) no. 1, pp. 174-181. doi: 10.4153/S000843952000034X
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     author = {Betsakos, Dimitrios and Karafyllia, Christina and Karamanlis, Nikolaos},
     title = {Hyperbolic metric and membership of conformal maps in the {Bergman} space},
     journal = {Canadian mathematical bulletin},
     pages = {174--181},
     year = {2021},
     volume = {64},
     number = {1},
     doi = {10.4153/S000843952000034X},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S000843952000034X/}
}
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%T Hyperbolic metric and membership of conformal maps in the Bergman space
%J Canadian mathematical bulletin
%D 2021
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