Counterexamples on \(L_p\)-maximal regularity
type: Item
instance of: scholarly article
title: Counterexamples on \(L_p\)-maximal regularity
zbMATH Open document ID: 0927.47010
DOI: 10.1007/PL00004688
author: Christian Le Merdy
published in: Mathematische Zeitschrift
publication date: 1999-12-06T00:00:00Z
review text: We establish a transference result for \(L^p\)-maximal regularity for the abstract Cauchy problem on Banach space. From this result, we deduce counterexamples to \(L^p\)-maximal regularity \((1<p<\infty)\). In particular, we obtain an operator \(B\) without any \(L^p\)-maximal regularity although it admits bounded imaginary powers with \(\| B^{is}\|= 1\) for all real numbers \(s\). We also derive an operator which satisfies \(L^p\)-maximal regularity on bounded intervals \([0,T[\) but not on the half line \([0,+\infty[\).
reviewed by: Hitoshi Abe
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1336812
zbMATH Keywords: \(L^p\)-maximal regularity
zbMATH Keywords: abstract Cauchy problem
zbMATH Keywords: counterexamples
MaRDI profile type: Publication
Wikidata QID: Q124819497
full work available at URL: pl00004688
OpenAlex ID: W2003888156
description: scientific article; zbMATH DE number 1336812