[Noyaux reproduisants pour les espaces harmoniques de Besov sur la boule]
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.
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.
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@article{CRMATH_2009__347_13-14_735_0,
author = {Se\c{c}il Gerg\"un and H. Turgay Kaptano\u{g}lu and A. Ersin \"Ureyen},
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},
}
TY - JOUR AU - Seçil Gergün AU - H. Turgay Kaptanoğlu AU - A. Ersin Üreyen 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 DO - 10.1016/j.crma.2009.04.016 LA - en ID - CRMATH_2009__347_13-14_735_0 ER -
Seçil Gergün; H. Turgay Kaptanoğlu; A. Ersin Üreyen. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.016/
[1] Harmonic Function Theory, Springer, New York, 1992
[2] Representation theorems for holomorphic and harmonic functions in , Astérisque, Volume 77 (1980), pp. 12-66
[3] Harmonic Besov spaces on the unit ball of , Rocky Mountain J. Math., Volume 31 (2001), pp. 1305-1316
[4] The Sobolev spaces of harmonic functions, Studia Math., Volume 84 (1986), pp. 79-87
[5] Estimates in Sobolev norms for harmonic and holomorphic functions and interpolation between Sobolev and Hölder spaces of harmonic functions, Studia Math., Volume 86 (1987), pp. 255-271
[6] On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in , Studia Math., Volume 87 (1987), pp. 23-32
[7] On the space of Bloch harmonic functions and interpolation of spaces of harmonic and holomorphic functions, Studia Math., Volume 87 (1987), pp. 223-238
[8] Corrigendum to the paper “On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in ”, Studia Math., Volume 101 (1992), p. 319
[9] Reproducing kernels for harmonic Bergman spaces of the unit ball, Monatsh. Math., Volume 125 (1998), pp. 25-35
[10] Weighted Lipschitz continuity and harmonic Bloch and Besov spaces in the unit real ball, Proc. Edinb. Math. Soc., Volume 48 (2005), pp. 743-755
[11] Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ., Princeton, 1971
[12] On harmonic function spaces, J. Math. Soc. Japan, Volume 57 (2005), pp. 781-802
[13] Operators on harmonic Bergman spaces, Integral Equations Operator Theory, Volume 24 (1996), pp. 352-371
[14] A characterization of the harmonic Bloch space and the harmonic Besov spaces by an oscillation, Proc. Edinb. Math. Soc., Volume 45 (2002), pp. 229-239
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☆ This research is supported by TÜBİTAK under Research Project Grant 108T329.
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