Extrapolation and weighted norm inequalities between Lebesgue and Lipschitz spaces in the variable exponent context
type: Item
instance of: scholarly article
title: Extrapolation and weighted norm inequalities between Lebesgue and Lipschitz spaces in the variable exponent context
zbMATH Open document ID: 1339.46025
author: Adrián Cabral
author: Gladis Pradolini
author: Wilfredo Ramos
published in: Journal of Mathematical Analysis and Applications
publication date: 2016-01-28T00:00:00Z
review text: Several extrapolation results starting from weighted norm inequalities between Lebesgue and Lipschitz spaces given by \[ \sup_{B}\frac{\|w\chi_B\|_\infty}{|B|^{1+\delta/n}}\int_B|f(x)-m_B(f)|dx\leq C\|gw\|_s \] are obtained, where \(1<\beta<\infty\), \(0\leq\delta<1\), \(\delta/n=1/\beta-1/s\), \(f\) and \(g\) are two measurable functions and \(w\) belongs to a suitable class of weights. This hypothesis leads to a large class of inequalities for sublinear operators acting between weighted \(L^p\) and \(L^q\) spaces; weighted \(L^p\) and Lipschitz integral spaces; variable Lebesgue spaces \(L^{p(\cdot)}\) and \(L^{q(\cdot)}\); variable Lebesgue spaces \(L^{p(\cdot)}\) and variable versions of Lipschitz integral spaces. An important ingredient of the proofs is the new pointwise estimate \(f_\gamma^\#(x)\leq M_{\delta-\gamma}f_\delta^\#(x)\) for \(0\leq\gamma\leq\delta<1\), relating the fractional sharp maximal function \(f_\delta^\#\) and the fractional maximal function \(M_\delta f\).
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 6536926
zbMATH Keywords: variable exponent spaces
zbMATH Keywords: Lipschitz spaces
zbMATH Keywords: weights
zbMATH Keywords: maximal operator
zbMATH Keywords: fractional integrals
zbMATH Keywords: Rubio de Francia extrapolation
reviewed by: Oleksiy Karlovych
MaRDI profile type: Publication
full work available at URL: j.jmaa.2015.12.020
OpenAlex ID: W2209935620
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DOI: 10.1016/J.JMAA.2015.12.020
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description: scientific article; zbMATH DE number 6536926