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OSCILLATORY MULTIPLIERS RELATED TO THE WAVE EQUATION ON NONCOMPACT SYMMETRIC SPACES

Published online by Cambridge University Press:  24 March 2003

MICHAEL COWLING ,
S. GIULINI  and
STEFANO MEDA
MICHAEL COWLING
Affiliation:
School of Mathematics, University of New South Wales, UNSW Sydney, NSW 2052, Australiam.cowling@unsw.edu.au
S. GIULINI
Affiliation:
Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italygiulini@dima.unige.it
STEFANO MEDA
Affiliation:
Dipartimento di Statistica, Università di Milano-Bicocca, via Bicocca degli Arcimboldi 8, 20126 Milano, Italystemed@mate.polimi.it
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Abstract

This paper is devoted to the study of a family of oscillatory multipliers of the Laplace–Beltrami operator on symmetric spaces of the noncompact type. This family is related to the regularity (in space, for fixed time) of the solutions to the wave equation. Our method relies on estimates for the Poisson semigroup in complex time, which were obtained in our previous paper [6].

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 66 , Issue 3 , December 2002 , pp. 691 - 709
Copyright
© The London Mathematical Society, 2002

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Footnotes

Work supported by a Special Research Grant of the University of New South Wales, by the Australian Research Council, and by the Italian MURST, fondi 60%.