Reproducing kernels for harmonic Besov spaces on the ball

Gergün, Seçil; Kaptanoğlu, H. Turgay; Üreyen, A. Ersin

doi:10.1016/j.crma.2009.04.016

Mathematical Analysis/Harmonic Analysis

Reproducing kernels for harmonic Besov spaces on the ball
[Noyaux reproduisants pour les espaces harmoniques de Besov sur la boule]

Présenté par : Jean-Pierre Kahane

Gergün, Seçil ¹ ; Kaptanoğlu, H. Turgay ² ; Üreyen, A. Ersin ³

¹ Department of Mathematics and Computer Science, Çankaya University, Ankara 06530, Turkey
² Department of Mathematics, Bilkent University, Ankara 06800, Turkey
³ Department of Mathematics, Anadolu University, Eskişehir 26470, Turkey

Comptes Rendus. Mathématique, Tome 347 (2009) no. 13-14, pp. 735-738.

Résumé
Abstract

Les espaces de Besov de fonctions harmoniques sur la boule unité de $R^{n}$ sont défini en exigeant que suffisamment des dérivés de haut ordre de fonctions appartiennent aux espaces de Bergman harmoniques. Nous calculons les noyaux reproduisants de ces espaces de Besov qui sont des espaces de Hilbert. Les noyaux se révèlent être, de façon tout naturel, des sommes infinies pondérées des harmoniques zonalles et des dérivés fractionnels radiaux du noyau de Poisson.

Besov spaces of harmonic functions on the unit ball of $R^{n}$ are defined by requiring sufficiently high-order derivatives of functions lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels turn out to be weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel.

Reçu le : 2009-02-27
Accepté le : 2009-03-24
Publié le : 2009-05-09

DOI : 10.1016/j.crma.2009.04.016

Affiliations des auteurs :

Gergün, Seçil ¹ ; Kaptanoğlu, H. Turgay ² ; Üreyen, A. Ersin ³

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     title = {Reproducing kernels for harmonic {Besov} spaces on the ball},
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Gergün, Seçil; Kaptanoğlu, H. Turgay; Üreyen, A. Ersin. Reproducing kernels for harmonic Besov spaces on the ball. Comptes Rendus. Mathématique, Tome 347 (2009) no. 13-14, pp. 735-738. doi : 10.1016/j.crma.2009.04.016. http://archive.numdam.org/articles/10.1016/j.crma.2009.04.016/

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^☆ This research is supported by TÜBİTAK under Research Project Grant 108T329.