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VOL. 45 | 2013 Boundedness of maximal functions on non-doubling manifolds with ends
Xuan Thinh Duong, Ji Li, Adam Sikora

Editor(s) Xuan Duong, Jeff Hogan, Chris Meaney, Adam Sikora

Abstract

Let $M$ be a manifold with ends constructed in $[2]$ and $\Delta$ be the Laplace-Beltrami operator on $M$. In this note, we show the weak type $(1,1)$ and $L^p$ boundedness of the Hardy-Littlewood maximal function and of the maximal function associated with the heat semigroup $\mathcal{M}_{\Delta}f(x) = sup_{t \gt o} | exp(-t \Delta)f(x)|$ on $L^p(M)$ for $1 \lt p \leq \infty$. The significance of these results comes from the fact that $M$ does not satisfies the doubling condition.

Information

Published: 1 January 2013
First available in Project Euclid: 3 December 2014

zbMATH: 1337.42018
MathSciNet: MR3424866

Rights: Copyright © 2013, 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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