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Université d'Orléans |  |
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Université d'Orléans | |
| HAL: hal-00005820, version 1 |
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| Colloquium Mathematicum 80 (1999) 63-82 |
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| Harmonic Functions on the Real Hyperbolic Ball I : Boundary Values and Atomic Decompositions of Hardy Spaces |
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| Philippe Jaming 1 |
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| (1999) |
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| In this article we study harmonic functions for the Laplace-Beltrami operator on the real hyperbolic space $\B_n$. We obtain necessary and sufficient conditions for this functions and their normal derivatives to have a boundary distribution. In doing so, we put forward different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball $\B_n$. We then study Hardy spaces $H^p(\B_n)$, $0< p <\infty$, whose elements appear as the hyperbolic harmonic extensions of distributions belonging to the Hardy spaces of the sphere $H^p(\S^{n-1})$. In particular, we obtain an atomic decomposition of this spaces. |
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| 1: | Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO) |
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Université d'Orléans – CNRS : UMR7349 |
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| Subject | : | Mathematics/Classical Analysis and ODEs |
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| real hyperbolic ball – harmonic functions – boundary values – Hardy spaces – atomic decomposition |
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| hal-00005820, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00005820 | |
| oai:hal.archives-ouvertes.fr:hal-00005820 | |
| From: Philippe Jaming | |
| Submitted on: Monday, 4 July 2005 19:11:06 | |
| Updated on: Tuesday, 12 July 2005 11:14:35 | |
