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Extension of vector-valued holomorphic and harmonic functions

Volume 183 / 2007

José Bonet, Leonhard Frerick, Enrique Jordá Studia Mathematica 183 (2007), 225-248 MSC: 46E40, 46A04. DOI: 10.4064/sm183-3-2

Abstract

We present a unified approach to the study of extensions of vector-valued holomorphic or harmonic functions based on the existence of weak or weak$^*$-holomorphic or harmonic extensions. Several recent results due to Arendt, Nikolski, Bierstedt, Holtmanns and Grosse-Erdmann are extended. An open problem by Grosse-Erdmann is solved in the negative. Using the extension results we prove existence of Wolff type representations for the duals of certain function spaces.

Authors

  • José BonetDepartamento de Matemática Aplicada
    and IMPA-UPV
    ETS Arquitectura
    Universidad Politécnica de Valencia
    E-46071 Valencia, Spain
    e-mail
  • Leonhard FrerickFB IV – Mathematik
    Universität Trier
    D-54286 Trier, Germany
    e-mail
  • Enrique JordáDepartamento de Matemática Aplicada
    and IMPA-UPV
    E. Politécnica Superior de Alcoy
    Universidad Politécnica de Valencia
    Plaza Ferrándiz y Carbonell 2
    E-03801 Alcoy (Alicante), Spain
    e-mail

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