Composition operators between Bergman and Hardy spaces

1996/01/01 by Wayne Smith · 8 citations
Mathematics · #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Algebraic and Geometric Analysis

paper · pdf · doi:10.1090/s0002-9947-96-01647-9

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.

Citations

• The Essential Norm of a Composition Operator

Cited by

• Hyperbolic metric and membership of conformal maps in the Bergman space
• Geometric characterizations for conformal mappings in weighted Bergman spaces
• Generalized weighted composition operators on Bergman spaces induced by doubling weights
• The Bergman number of a plane domain
• Eigenvalues for Infinitesimal Generators of Semigroups of Composition Operators
• Dyadic Carleson embedding and sparse domination of weighted composition operators on strictly pseudoconvex domains
• Hardy and Bergman spaces on hyperconvex domains and their composition operators
• Compact Differences of Weighted Composition Operators

Related

• Compact composition operators on weighted Hilbert spaces of analytic\n functions
• Composition operators on weighted Bergman spaces of Dirichlet series
• Generalized weighted composition operators on Bergman spaces induced by doubling weights
• Composition operators on the polydisc
• The weighted composition operators on the large weighted Bergman spaces