Besov spaces, multipliers and univalent functions
type: Item
instance of: scholarly article
title: Besov spaces, multipliers and univalent functions
zbMATH Open document ID: 1293.30092
author: Petros Galanopoulos
author: Daniel Girela
author: María J. Martín
published in: Complex Analysis and Operator Theory
publication date: 2013-10-10T00:00:00Z
review text: For \(1\leq p<\infty\), let \(B^p\) denote the Besov spaces of holomorphic functions in the unit disk, and let \(B\) denote the Bloch space. The authors consider \(M(B^p,B^q)\) and \(M(B^p,B)\), the spaces of multipliers from \(B^p\) to \(B^q\) and \(B\), respectively, for \(1\leq p,q<\infty\), and they find characterizations of these spaces, without use of capacity. The authors investigate ``which functions of certain important types (lacunary series, univalent functions, `modified' inner functions) are to be found in the spaces \(M(B^p,B^q)\)''. Studying lacunary series as \(M(B^p,B^q)\) members, the authors are able to give a negative answer to the problem stated in [\textit{N. Zorboska}, in: More progresses in analysis. Proceedings of the 5th international ISAAC congress, Catania, Italy, July 2005. Hackensack, NJ: World Scientific. 387--396 (2009; Zbl 1192.47026)].
Mathematics Subject Classification ID: 30H25
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 30C35
zbMATH DE Number: 6214961
zbMATH Keywords: Besov spaces
zbMATH Keywords: Bloch space
zbMATH Keywords: Möbius invariant spaces
zbMATH Keywords: multiplication operator
zbMATH Keywords: univalent functions
MaRDI profile type: Publication
full work available at URL: s11785-011-0160-3
OpenAlex ID: W2132224950
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Besov spaces, multipliers and univalent functions (DOI)
DOI: 10.1007/S11785-011-0160-3