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Fourier Integral Operators on Noncompact Symmetric Spaces of Real Rank One

✍ Scribed by Alexandru D. Ionescu

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 217 KB
Volume: 174
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2000.3572

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✦ Synopsis

Let X=GÂK be a noncompact symmetric space of real rank one. The purpose of this paper is to investigate L p boundedness properties of a certain class of radial Fourier integral operators on the space X. We will prove that if u { is the solution at some fixed time { of the natural wave equation on X with initial data f and g and 1<p< , then

). We will obtain both the precise behavior of the norm C p ({) and the sharp regularity assumptions on the functions f and g (i.e., the exponent b p ) that make this inequality possible. In the second part of the paper we deal with the analog of E. M. Stein's maximal spherical averages and prove exponential decay estimates (of a highly non-euclidean nature) on the L p norm of sup T { T+1 | f V d_ { (z)|, where d_ { is a normalized spherical measure.

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