On variable exponent Lebesgue spaces of entire analytic functions
type: Item
instance of: scholarly article
title: On variable exponent Lebesgue spaces of entire analytic functions
zbMATH Open document ID: 1244.46008
author: Joaquín Motos
author: María Jesús Planells
author: C. F. Talavera
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-02-27T00:00:00Z
review text: The authors introduce the variable Lebesgue spaces of entire functions \(L^K_{p(\cdot)}\), where \(K\) is a compact subset of \({\mathbb R}^n\). They obtain a generalization of the maximal inequality of Jawerth and inequalities of Plancherel-Polya-Nikolskii type. They calculate the dual of the space \(L^K_{p(\cdot)}\) when the function \(\chi_K\) is an \(L_{p(\cdot)}\)-Fourier multiplier and give a number of consequences of this result (on sequence space representations). Finally, a Fourier multiplier theorem by Triebel is extended to the setting of variable exponent Lebesgue spaces.
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 42B15
zbMATH DE Number: 6009597
zbMATH Keywords: variable exponent
zbMATH Keywords: Lebesgue spaces
zbMATH Keywords: \(L_p\)-spaces of entire analytic functions
zbMATH Keywords: maximal operators
zbMATH Keywords: Fourier multipliers
reviewed by: Sergei S. Platonov
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.09.069
OpenAlex ID: W2030129865
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DOI: 10.1016/J.JMAA.2011.09.069
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description: scientific article; zbMATH DE number 6009597