Restricted weak-type Rubio de Francia extrapolation for \(p>p_{0}\) with applications to exponential integrability estimates
type: Item
instance of: scholarly article
title: Restricted weak-type Rubio de Francia extrapolation for \(p>p_{0}\) with applications to exponential integrability estimates
zbMATH Open document ID: 1343.42029
author: Javier Soria
author: María J. Carro
published in: Advances in Mathematics
publication date: 2016-02-02T00:00:00Z
review text: Let \(p\in[1,\infty)\) and \(\widehat{A}_p\) be the class of weights \(\omega\) of the form \(\omega:=(Mg)^{1-p}u\) for some \(g\in L^1_{\mathrm{loc}}(\mathbb{R}^n)\) and \(u\in A_1\), where \(A_1\) represents the class of \(A_1\) weights and \(M\) is the Hardy-Littlewood maximal operator. For any \(p\in[1,\infty)\) and \(q\in[1,\infty]\), denote the Lorentz spaces associated with weights \(v\in\widehat{A}_p\) by \(L^{p,q}(v)\). The authors show that, if \(p_0\in(1,\infty)\) and \(T\) is a sublinear operator such that, for every \(v\in\widehat{A}_p\), \(T\) is bounded from \(L^{p_0,1}(v)\) into \(L^{p_0,\infty}(v)\) with a constant less than or equal to \(\varphi(\| v\|_{\widehat{A}_{p_0}})\) for some increasing function \(\varphi\) on \((0,\infty)\), then for every \(p\in(p_0,\infty)\) and every \(v\in\widehat{A}_p\), \(T\) is bounded from \(L^{p,1}(v)\) into \(L^{p,\infty}(v)\) with a precise control of the constant depending on \(\|v\|_{\widehat{A}_p}\) and \(\varphi\). As applications, exponential integrability estimates are proved for several classes of operators appearing in harmonic analysis, such as square functions, Haar shift operators, maximal Calderón-Zygmund operators, etc.
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 6538735
zbMATH Keywords: Lorentz spaces
zbMATH Keywords: Rubio de Francia extrapolation
zbMATH Keywords: \(A_p\) weights
zbMATH Keywords: restricted weak-type estimates
zbMATH Keywords: Hardy-Littlewood maximal function
zbMATH Keywords: exponential integrability
zbMATH Keywords: square functions
zbMATH Keywords: Haar shift operators
zbMATH Keywords: maximal Calderón-Zygmund operators
reviewed by: Dachun Yang
MaRDI profile type: Publication
full work available at URL: j.aim.2015.12.013
OpenAlex ID: W2232201666
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DOI: 10.1016/J.AIM.2015.12.013
description: scientific article; zbMATH DE number 6538735