Maximal operator with rough kernel in variable Musielak-Morrey-Orlicz type spaces, variable Herz spaces and grand variable Lebesgue spaces
type: Item
instance of: scholarly article
title: Maximal operator with rough kernel in variable Musielak-Morrey-Orlicz type spaces, variable Herz spaces and grand variable Lebesgue spaces
zbMATH Open document ID: 1387.42020
author: Humberto Rafeiro
author: S. G. Samko
published in: Integral Equations and Operator Theory
publication date: 2017-12-07T00:00:00Z
review text: Let us consider the maximal operator \(M_{\Omega}\), defined for a function \(f\) in \(\mathbb{R}^n,\) as follows \[ M_{\Omega} f(x):= \sup_{r>0} \int_{|y|< r} |\Omega(y)| f(x-y) \;dy, \] which is related to a kernel function \(\Omega\) in \(L^1(\mathbb{S}^{n-1})\), homogeneous of degree \(0\). The boundedness of \(M_{\Omega}\) in some non-standard function spaces is considered, such as generalized variable exponent Morrey spaces, generalized Orlicz-Morrey, complementary generalized Morrey or variable exponent Herz spaces. Although the classical rotation method is not applicable in this context, the general technique applied is based on rescaling properties of these spaces. The results obtained are new, even for the counterpart spaces that have \(p\) as a constant exponent.
reviewed by: Santiago Boza
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 6816337
zbMATH Keywords: rough operator
zbMATH Keywords: maximal operator
zbMATH Keywords: generalized Orlicz-Morrey spaces
zbMATH Keywords: generalized variable Morrey spaces
zbMATH Keywords: variable Herz spaces
MaRDI profile type: Publication
full work available at URL: s00020-017-2398-2
OpenAlex ID: W2745511316
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DOI: 10.1007/S00020-017-2398-2
description: scientific article; zbMATH DE number 6816337