Harmonic functions on the real hyperbolic ball II Hardy and Lipschitz spaces

Details Harmonic functions on the real hyperbolic ball II Hardy and Lipschitz spaces Harmonic functions on the real hyperbolic ball II Hardy and Lipschitz spaces

1999-02-08

arxiv.org/abs/math/9902053v1

Mathematics

Classical Analysis and ODEs

29 pages, 5 figures, LATEX file Authors partially supported by the "European Commission" (TMR 1998-2001 Network Harmonic Analy

Scientific paper

In this paper, we pursue the study of harmonic functions on the real hyperbolic ball started by the second named author. Our focus here is on the theory of Hardy, Hardy-Sobolev and Lipschitz spaces of these functions. We prove here that these spaces admit Fefferman-Stein like characterizations in terms of maximal and square functionals. We further prove that the hyperbolic harmonic extension of Lipschitz functions on the boundary extend into Lipschitz functions on the whole ball.

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