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VOL. 39 | 2001 Spectral multipliers for self-adjoint operators
Xuan Thinh Duong, El Maati Ouhabaz, Adam Sikora

Editor(s) Andrew Hassell, Alexander Isaev, Adam Sikora


In this article, we give a survey of spectral multipliers and present (without proof) sharp Hörmander-type multiplier theorems for a self adjoint operator $A$ under the assumption that $A$ has Gaussian heat kernel bounds and satisfies appropriate estimates of the $L^2$ norm of the kernels of spectral multipliers. Our theorems imply several important, previously known results on spectral multipliers and give new results for sharp estimates for the critical exponent for the Riesz means summability.


Published: 1 January 2001
First available in Project Euclid: 17 November 2014

zbMATH: 1118.43300
MathSciNet: MR1852695

Rights: Copyright © 2001, 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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