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VOL. 41 | 2003 Weak type $(1,1)$ estimates of maximal truncated singular operators
Xuan Thinh Duong, Lixin Yan

Editor(s) Xuan Thinh Duong, Alan Pryde


Let $X$ be a space of homogeneous type and $T$ a singular integral operator which is bounded on $L^2(X)$. We give a sufficient condition on the kernel of $T$ so that the maximal truncated operator $T_*$, which is defined by $T_*f(x) = sup_{\epsilon\lt0} |T_\epsilonf(x)|$, to be of weak type (1, 1). Our condition is weaker than the usual Hörmander type condition. Applications include the dominated convergence theorem of holomorphic functional calculi of linear elliptic operators on irregular domains.


Published: 1 January 2003
First available in Project Euclid: 18 November 2014

zbMATH: 1151.42305
MathSciNet: MR1994514

Rights: Copyright © 2003, 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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