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Sharp Norm Estimates for the Bergman Operator from Weighted Mixed-norm Spaces to Weighted Hardy Spaces

  Published:2016-04-18
 Printed: Dec 2016
  • Carme Cascante,
    Dept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
  • Joan Fàbrega,
    Dept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
  • Joaquín M. Ortega,
    Dept. Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain
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Abstract

In this paper we give sharp norm estimates for the Bergman operator acting from weighted mixed-norm spaces to weighted Hardy spaces in the ball, endowed with natural norms.
Keywords: weighted Hardy space, Bergman operator, sharp norm estimate weighted Hardy space, Bergman operator, sharp norm estimate
MSC Classifications: 47B38, 32A35, 42B25, 32A37 show english descriptions Operators on function spaces (general)
$H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
Maximal functions, Littlewood-Paley theory
Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]
47B38 - Operators on function spaces (general)
32A35 - $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
42B25 - Maximal functions, Littlewood-Paley theory
32A37 - Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx]
 

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