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Weighted spaces of harmonic and holomorphic functions: sequence space representations and protective descriptions

Published online by Cambridge University Press:  20 January 2009

Päivi Mattila ,
Eero Saksman  and
Jari Taskinen
Päivi Mattila
Affiliation:
Department of Mathematics, P.O. Box 4 (Hallituskatu 15), Fin-00014, University of Helsinki, Finland
Eero Saksman
Affiliation:
Department of Mathematics, P.O. Box 4 (Hallituskatu 15), Fin-00014, University of Helsinki, Finland
Jari Taskinen
Affiliation:
Department of Mathematics, P.O. Box 4 (Hallituskatu 15), Fin-00014, University of Helsinki, Finland
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Abstract

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We study the structure of inductive limits of weighted spaces of harmonic and holomorphic functions defined on the open unit disk of ℂ, and of the associated weighted locally convex spaces. Using a result of Lusky we prove, for certain radial weights on the open unit disk D of ℂ, that the spaces of harmonic and holomorphic functions are isomorphic to complemented subspaces of the corresponding Köthe sequence spaces. We also study the spaces of harmonic functions for certain non-radial weights on D. We show, under a natural sufficient condition for the weights, that the spaces of harmonic functions on D are isomorphic to corresponding spaces of continuous or bounded functions on ∂D.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 1 , February 1997 , pp. 41 - 62
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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