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:

Bergman spaces, hyperbolic metric, Lipschitz condition Bergman spaces, hyperbolic metric, Lipschitz condition

MSC Classifications:

32A36 show english descriptions Bergman spaces 32A36 - Bergman spaces

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