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VOL. 44 | 2010 Stability in $p$ of the $H^\infty$-Calculus of First-Order Systems in $L^p$
Tuomas Hytönen, Alan McIntosh

Editor(s) Andrew Hassell, Alan McIntosh, Robert Taggart


We study certain differential operators of the form $AD$ arising from a first-order approach to the Kato square root problem. We show that if such operators are$R$-bisectorial in $L^p$, they remain $R-bisectorial in $L^q$ for all $q$ close to $p$.In combination with our earlier results with Portal, which required such $R$-bisectoriality in different $L^q$ spaces to start with, this shows that the $R$-bisectoriality in just one $L^p$ actually implies bounded $H^\infty$-calculus in $L^q$ for all $q$ close to $p$. We adapt the approach to related second-order results developed by Auscher, Hofmann and Martell, and also employ abstract extrapolation theorems due to Kalton and Mitrea


Published: 1 January 2010
First available in Project Euclid: 18 November 2014

zbMATH: 1252.47014
MathSciNet: MR2655384

Rights: Copyright © 2010, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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