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TIME AVERAGES FOR THE LAPLACE GROUP

Published online by Cambridge University Press:  15 February 2005

Damian C. Jackson
Damian C. Jackson
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK ([email protected])
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Abstract

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The imaginary powers of the Laplace operator over the circle give a $C_0$ group of bounded linear operators on $\mathsf{L}_{\theta}^p(0,2\pi)$ ($1\ltp\lt\infty$). Whereas the group is unbounded on $\mathsf{L}^4$, this paper shows that the $\mathsf{L}^4$ long-time averages of each $f$ in $\mathsf{L}^2$ are bounded. This is a Fourier restriction phenomenon.

AMS 2000 Mathematics subject classification: Primary 42A15; 42B15

Keywords

imaginary powers of the Laplace operatorRiesz potentialsFourier restriction phenomena
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 1 , February 2005 , pp. 143 - 149
Copyright
Copyright © Edinburgh Mathematical Society 2005