Extrapolation theory for the real interpolation method.
type: Item
instance of: scholarly article
title: Extrapolation theory for the real interpolation method.
zbMATH Open document ID: 1034.46077
author: Joaquim Martin
author: María J. Carro
published in: Collectanea Mathematica
publication date: 2003-06-30T00:00:00Z
full work available at URL: https://eudml.org/doc/42902
review text: The first author has recently obtained improvements to a result of Yano on sublinear operators \(T\) mapping \(L\log L(\mu)\) into \(L^1(\nu)\) (when \(\mu\), \(\nu\) are finite measures) and one of Zygmund on linear operators mapping \(L^\infty(\mu)\) into \(L_{\exp}(\nu)\). In the present paper, the authors develop an abstract extrapolation theory for the real interpolation method that gives a better range space in the case of a Yano-type result and a better domain space in the case of a Zygmund-type result. The method also gives new endpoint estimates of the Sobolev embedding theorem for an arbitrary domain. The identification of the extrapolation spaces is readily made in the theory, and this means that it is easy to apply.
Mathematics Subject Classification ID: 46M35
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1943353
zbMATH Keywords: real interpolation
zbMATH Keywords: extrapolation
zbMATH Keywords: Yano's theorem
zbMATH Keywords: Zygmund's theorem
zbMATH Keywords: Sobolev embeddings
reviewed by: W. D. Evans
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1943353