Muckenhoupt weights and maximal \(L^p\)-regularity
type: Item
instance of: scholarly article
title: Muckenhoupt weights and maximal \(L^p\)-regularity
zbMATH Open document ID: 1108.35100
author: Robert Haller
author: Horst Heck
author: Matthias Hieber
published in: Archiv der Mathematik
publication date: 2004-03-07T00:00:00Z
review text: For \(X\) a Banach space, \(q\in(1,\infty)\), \(f\in L^q(\mathbb R_+,X)\), consider the equation \(u'(t)+Au(t)=f(t)\) with a sectorial operator \(-A\) of angle \(<\pi/2\). The operator \(A\) is of maximal regularity, if for any \(f\in L^q(\mathbb R_+,X)\) both \(u'\) and \(Au\) are also in \(L^q(\mathbb R_+,X)\). This property is independent of \(q\in(1,\infty)\). In the current paper, sufficient conditions for maximal regularity are given in terms of weighted \(L^p\)-estimates (with weight belonging to some Muckenhoupt class) for a sublinear operator dominating \(is(is+A)^{-1}\) for all \(s\in \mathbb R\). The results are applied to elliptic differential operators with continuous top order coefficients.
reviewed by: Andreas Gastel
Mathematics Subject Classification ID: 35K90
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35J45
zbMATH DE Number: 2051620
zbMATH Keywords: Muckenhoupt class
zbMATH Keywords: elliptic differential operator
zbMATH Keywords: sectorial operator
zbMATH Keywords: maximal regularity
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2051620