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Weighted Composition Operators Associated with Conformal Mappings

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Quadrature Domains and Their Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 156))

Abstract

For conformal self-maps ϕ of the unit disk, we study weighted composition operators f ↦ f ϕ · (ϕ′)b . We are interested in their boundedness, compactness and contractivity properties as operators acting in weighted Djrbashian-Bergman spaces.

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Author information

Authors and Affiliations

  1. Matematik Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Serguei Shimorin

Authors
  1. Serguei Shimorin
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA

    Peter Ebenfelt

  2. Department of Mathematics, Royal Institute of Technology (KTH), 100 44, Stockholm, Sweden

    Björn Gustafsson

  3. Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR, 72701, USA

    Dmitry Khavinson

  4. Mathematics Department, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA

    Mihai Putinar

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Shimorin, S. (2005). Weighted Composition Operators Associated with Conformal Mappings. In: Ebenfelt, P., Gustafsson, B., Khavinson, D., Putinar, M. (eds) Quadrature Domains and Their Applications. Operator Theory: Advances and Applications, vol 156. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7316-4_11

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