Besov spaces of harmonic functions on the unit ball of 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.
Les espaces de Besov de fonctions harmoniques sur la boule unité de 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.
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@article{CRMATH_2009__347_13-14_735_0,
author = {Gerg\"un, Se\c{c}il and Kaptano\u{g}lu, H. Turgay and \"Ureyen, A. Ersin},
title = {Reproducing kernels for harmonic {Besov} spaces on the ball},
journal = {Comptes Rendus. Math\'ematique},
pages = {735--738},
publisher = {Elsevier},
volume = {347},
number = {13-14},
year = {2009},
doi = {10.1016/j.crma.2009.04.016},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.04.016/}
}
TY - JOUR AU - Gergün, Seçil AU - Kaptanoğlu, H. Turgay AU - Üreyen, A. Ersin TI - Reproducing kernels for harmonic Besov spaces on the ball JO - Comptes Rendus. Mathématique PY - 2009 SP - 735 EP - 738 VL - 347 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.04.016/ DO - 10.1016/j.crma.2009.04.016 LA - en ID - CRMATH_2009__347_13-14_735_0 ER -
%0 Journal Article %A Gergün, Seçil %A Kaptanoğlu, H. Turgay %A Üreyen, A. Ersin %T Reproducing kernels for harmonic Besov spaces on the ball %J Comptes Rendus. Mathématique %D 2009 %P 735-738 %V 347 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.04.016/ %R 10.1016/j.crma.2009.04.016 %G en %F CRMATH_2009__347_13-14_735_0
Gergün, Seçil; Kaptanoğlu, H. Turgay; Üreyen, A. Ersin. Reproducing kernels for harmonic Besov spaces on the ball. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 735-738. doi : 10.1016/j.crma.2009.04.016. http://www.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.
