On generalized Bergman spaces

Wolfgang Lusky

ArticleOriginal scientific text

Title

On generalized Bergman spaces

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Affiliations

Fachbereich 17, Universität-Gesamthochschule, Warburger Straße 100, D-33098 Paderborn, Germany

Abstract

Let D be the open unit disc and μ a positive bounded measure on [0,1]. Extending results of Mateljević/Pavlović and Shields/Williams we give Banach-space descriptions of the classes of all harmonic (holomorphic) functions f: D → ℂ satisfying

ʃ_{0}^{1} {(ʃ_{0}^{2 π} {| f (r e^{i φ}) |}^{p} d φ)}^{\frac{q}{p}} d μ (r) < \infty

.

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Title

On generalized Bergman spaces

Affiliations

Abstract

Bibliography