New extrapolation estimates
type: Item
instance of: scholarly article
title: New extrapolation estimates
zbMATH Open document ID: 0962.42014
published in: Journal of Functional Analysis
publication date: 2001-01-11T00:00:00Z
review text: In this paper, the author gives several types of extrapolation results. One of them allows the author to improve Yano's extrapolation theorem. Given a sublinear operator \(T\) satisfying \[ \|T\chi_A\|_{L^p(\nu)}\leq \frac{C}{p-1}\|\chi_A\|_{L^p(\mu)}, \] for every measurable set \(A\) and every \(1<p\leq p_0\), with \(C\) independent of \(A\) and \(p\), we show that \[ \sup_{r>0}\frac{\int^\infty_{1/r}\lambda^\nu_{Tf}(y)\,dy}{1+\log^+ r}\lesssim\int_{\mathcal M}|f(x)|(1+\log^+|f(x)|)\,d\mu(x). \]
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46M35
zbMATH DE Number: 1502204
zbMATH Keywords: sublinear operator
zbMATH Keywords: extrapolation estimate
zbMATH Keywords: distribution function
author: María J. Carro
reviewed by: Dachun Yang
MaRDI profile type: Publication
full work available at URL: jfan.2000.3568
OpenAlex ID: W2014056304
cites work: Q4039801
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DOI: 10.1006/JFAN.2000.3568
description: scientific article; zbMATH DE number 1502204