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On Weighted Spaces of Harmonic and Holomorphic Functions
Author(s) -
Lusky Wolfgang
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.2.309
Subject(s) - holomorphic function , mathematics , harmonic function , bounded function , pure mathematics , harmonic , space (punctuation) , bounded mean oscillation , projection (relational algebra) , hardy space , mathematical analysis , identity theorem , computer science , physics , algorithm , quantum mechanics , operating system
Weighed spaces of harmonic and holomorphic functions on the unit disc are studied. We show that for all radial weights which are not decreasing too fast the space of harmonic functions is isomorphic to c 0 . For the weights that we consider we completely characterize those spaces of holomorphic functions which are isomorphic to c 0 . Moreover, we determine when the Riesz projection, mapping the weighted space of harmonic functions onto the corresponding space of holomorphic functions, is bounded.