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ArticleOriginal scientific text

Title

Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

Authors 1

Affiliations

  1. Département de Mathématiques, Faculté des Sciences, Université d'Orléans, BP 6759, F-45067 Orléans Cedex 2, France

Abstract

We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space _n. We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball _n. We then study the Hardy spaces Hp(_n), 0

Keywords

ENG
Hardy spaces, atomic decomposition, real hyperbolic ball, boundary values, harmonic functions

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Colloquium Mathematicum
1999/80/1
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Pages:
63-82
Main language of publication
English
Received
1998-08-25
Published
1999
Exact and natural sciences