Composition operators that improve integrability on weighted Bergman spaces

Smith, Wayne; Yang, Liming

doi:10.1090/S0002-9939-98-04206-3

Composition operators that improve integrability on weighted Bergman spaces
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by Wayne Smith and Liming Yang PDF

Proc. Amer. Math. Soc. 126 (1998), 411-420 Request permission

Abstract:

Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.

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