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Journal of Function Spaces and Applications
Volume 2013, Article ID 178460, 6 pages
http://dx.doi.org/10.1155/2013/178460
Research Article

Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions

Departamento de Matemática Aplicada, E. Politécnica Superior de Alcoy, Universidad Politécnica de Valencia, Plaza Ferrándiz y Carbonell 2, 03801 Alcoy, Spain

Received 30 May 2013; Accepted 3 August 2013

Academic Editor: Miguel Martin

Copyright © 2013 Enrique Jordá and Ana María Zarco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For an arbitrary open subset or and a continuous function we show that the space of weighed harmonic functions is almost isometric to a (closed) subspace of , thus extending a theorem due to Bonet and Wolf for spaces of holomorphic functions on open sets . Inspired by recent work of Boyd and Rueda, we characterize in terms of the extremal points of the dual of when is isometric to a subspace of . Some geometric conditions on an open set and convexity conditions on a weight on are given to ensure that neither nor are rotund.