Reproducing kernels for harmonic Besov spaces on the ball
type: Item
instance of: scholarly article
title: Reproducing kernels for harmonic Besov spaces on the ball
zbMATH Open document ID: 1179.31003
author: Seçil Gergün
author: H. Turgay Kaptanoğlu
author: Adem Ersin Üreyen
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2009-06-30T00:00:00Z
full work available at URL: http://hdl.handle.net/11693/11761
review text: The authors consider Besov spaces of harmonic functions on the unit ball \(\mathbb{B\subset R}^{n}\). They form a two parameter Sobolev type subfamily of harmonic functions on the unit ball \(\mathbb{B}\), extending Bergman spaces. Earlier such functions were studied by \textit{E. Ligocka} [Stud. Math. 84, 79--87 (1986; Zbl 0627.46033)], [Stud. Math. 86, 255--271 (1987; Zbl 0642.46035)], [Stud. Math. 87, 23--32 (1987; Zbl 0658.31006)], and [Stud. Math. 87, 223--238 (1987; Zbl 0657.31006)]. In the main result, the reproducing kernels of those Besov spaces which are Hilbert spaces are computed. They are weighted sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel, extending results of \textit{R. R. Coifman} and \textit{R. Rochberg} [Astérisque 77, 11--66 (1980; Zbl 0472.46040)] and \textit{S. Axler, P. Bourdon} and \textit{W. Ramey} [Harmonic function theory. Graduate Texts in Mathematics. 137. New York: Springer-Verlag. xii, 231 p. (1992; Zbl 0765.31001)].
Mathematics Subject Classification ID: 31B10
zbMATH DE Number: 5571954
zbMATH Keywords: Bergman spaces
zbMATH Keywords: Besov spaces
zbMATH Keywords: reproducing kernels
zbMATH Keywords: harmonic functions on the unit ball
MaRDI profile type: Publication
OpenAlex ID: W2087044225
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DOI: 10.1016/J.CRMA.2009.04.016
description: scientific article; zbMATH DE number 5571954