On generalized Bergman spaces

Volume 119 / 1996

Wolfgang Lusky Studia Mathematica 119 (1996), 77-95 DOI: 10.4064/sm-119-1-77-95


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 $ʃ_{0}^{1} (ʃ_{0}^{2π} |f(re^{iφ})|^p dφ)^{q/p} dμ(r) < ∞$.


  • Wolfgang Lusky

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