Singular integrals and potentials in some Banach function spaces with variable exponent
type: Item
instance of: scholarly article
title: Singular integrals and potentials in some Banach function spaces with variable exponent
zbMATH Open document ID: 1085.42008
DOI: 10.1155/2003/932158
author: Vakhtang Kokilashvili
author: S. G. Samko
published in: Journal of Function Spaces and Applications
publication date: 2004-10-28T00:00:00Z
review text: In the paper under review, the authors define a weighted version of the rearrangement invariant Banach function spaces of Lorentz type \(\Lambda_{w} ^{p(\cdot)}(\Omega)\), defined by the norm \(\| f\| _{\Lambda ^{p(\cdot)}(\Omega)} = \| w f^{**}\| _{L^{p(\cdot)}(\Omega)}\), were \(f^{**}\) is the maximal function of the decreasing rearrangement \(f^*\) of \(f\) and \(L^{p(\cdot)}(\Omega)\) denotes the Lebesgue space of measurable functions with variable exponent on a bounded set \(\Omega\) from \( \mathbb{R}^{n}\). If the variable exponent \(p(t)\) satisfies the so-called logarithmic Dini conditions they prove the boundedness of singular integrals, fractional integrals and Cauchy singular operators associated to Lyapunov curves and to bounded rotation curves without cusps.
reviewed by: Amiran Gogatishvili
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 2111353
zbMATH Keywords: Banach function space
zbMATH Keywords: non-increasing rearrangement
zbMATH Keywords: variable exponent
zbMATH Keywords: singular integral operators
zbMATH Keywords: Riesz potential
zbMATH Keywords: Lyapunov curve
zbMATH Keywords: curve of bounded rotation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2003/932158
OpenAlex ID: W2049733190
description: scientific article; zbMATH DE number 2111353