Composition operators between Bergman and Hardy spaces

Smith, Wayne

doi:10.1090/S0002-9947-96-01647-9

Composition operators between Bergman and Hardy spaces
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by Wayne Smith

Trans. Amer. Math. Soc. 348 (1996), 2331-2348

DOI: https://doi.org/10.1090/S0002-9947-96-01647-9

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Abstract:

We study composition operators between weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Particular choices for the weights yield results on composition operators between the classical unweighted Bergman and Hardy spaces.

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