Comptes Rendus
no. 13-14
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

Seçil Gergün1 ; H. Turgay Kaptanoğlu2 ; A. Ersin Üreyen3
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, Volume 347 (2009) no. 13-14, pp. 735-738.

Les espaces de Besov de fonctions harmoniques sur la boule unité de Rn 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 Rn 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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.04.016

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

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  • Karen Avetisyan Harmonic projections on Besov spaces in the real ball, Indian Journal of Pure and Applied Mathematics (2024) | DOI:10.1007/s13226-024-00558-8
  • Ömer Faruk Doğan Positive Toeplitz operators from a harmonic Bergman-Besov space into another, Banach Journal of Mathematical Analysis, Volume 16 (2022) no. 4, p. 36 (Id/No 70) | DOI:10.1007/s43037-022-00224-3 | Zbl:1515.47041
  • Ömer Doğan A class of integral operators induced by harmonic Bergman-Besov kernels on Lebesgue classes, Filomat, Volume 36 (2022) no. 13, p. 4293 | DOI:10.2298/fil2213293d
  • Ömer Faruk Doğan A class of integral operators from Lebesgue spaces into harmonic Bergman-Besov or weighted Bloch spaces, Hacettepe Journal of Mathematics and Statistics, Volume 50 (2021) no. 3, pp. 811-820 | DOI:10.15672/hujms.768123 | Zbl:1484.47049
  • H. Turgay Kaptanoğlu; A. Ersin Üreyen Kelvin-Möbius-invariant harmonic function spaces on the real unit ball, Journal of Mathematical Analysis and Applications, Volume 503 (2021) no. 1, p. 23 (Id/No 125298) | DOI:10.1016/j.jmaa.2021.125298 | Zbl:1470.31001
  • Ömer Faruk Doğan Harmonic Besov spaces with small exponents, Complex Variables and Elliptic Equations, Volume 65 (2020) no. 6, pp. 1051-1075 | DOI:10.1080/17476933.2019.1652277 | Zbl:1436.31013
  • Ömer Faruk Doğan; Adem Ersin Üreyen Inclusion relations between harmonic Bergman-Besov and weighted Bloch spaces on the unit ball., Czechoslovak Mathematical Journal, Volume 69 (2019) no. 2, pp. 503-523 | DOI:10.21136/cmj.2018.0422-17 | Zbl:1513.31005
  • Ömer Faruk Doğan; A. Ersin Üreyen Weighted harmonic Bloch spaces on the ball, Complex Analysis and Operator Theory, Volume 12 (2018) no. 5, pp. 1143-1177 | DOI:10.1007/s11785-017-0645-9 | Zbl:1395.31002
  • A. Ersin Üreyen Oscillation of holomorphic Bergman-Besov kernels on the ball, Monatshefte für Mathematik, Volume 184 (2017) no. 2, pp. 297-323 | DOI:10.1007/s00605-017-1043-0 | Zbl:1378.32002
  • Seçil Gergün; H. Turgay Kaptanoğlu; A. Ersin Üreyen Harmonic Besov spaces on the ball, International Journal of Mathematics, Volume 27 (2016) no. 9, p. 59 (Id/No 1650070) | DOI:10.1142/s0129167x16500701 | Zbl:1354.31005
  • Adem Ersin Üreyen An estimate of the oscillation of harmonic reproducing kernels with applications, Journal of Mathematical Analysis and Applications, Volume 434 (2016) no. 1, pp. 538-553 | DOI:10.1016/j.jmaa.2015.09.030 | Zbl:1358.46035
  • H. Turgay Kaptanoglu Reproducing kernels and radial differential operators for holomorphic and harmonic Besov spaces on unit balls: a unified view, Computational Methods and Function Theory, Volume 10 (2010) no. 2, pp. 483-500 | DOI:10.1007/bf03321777 | Zbl:1213.46026

Cité par 12 documents. Sources : Crossref, zbMATH

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

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