Norm Inequalities for Composition Operators on Hardy and Weighted Bergman Spaces

  • Christopher Hammond
  • Linda J. Patton
Part of the Operator Theory: Advances and Applications book series (OT, volume 202)


Any analytic self-map of the open unit disk induces a bounded composition operator on the Hardy space H 2 and on the standard weighted Bergman spaces A 2 β. For a particular self-map, it is reasonable to wonder whether there is any meaningful relationship between the norms of the corresponding operators acting on each of these spaces. In this paper, we demonstrate an inequality which, at least to a certain degree, provides an answer to this question.


Composition operator operator norm Hardy space weighted Bergman spaces Schur product 

Mathematics Subject Classification (2000)



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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Christopher Hammond
    • 1
  • Linda J. Patton
    • 2
  1. 1.Department of MathematicsConnecticut CollegeNew LondonUSA
  2. 2.Mathematics DepartmentCalifornia Polytechnic State UniversitySan Luis ObispoUSA

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