Estimates for the wave operator on the torus $\Pi ^n$
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- by Akos Magyar PDF
- Proc. Amer. Math. Soc. 125 (1997), 1969-1976 Request permission
Abstract:
We prove $L^{p’ }\rightarrow L^p$ bounds for the wave operator on the torus for large time. The new feature is the distribution of the singularities of the wave kernel, which can be understood by making use of Hardy-Littlewood method for exponential sums.References
- G. H. Hardy, Collected papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others). Vol. I, Clarendon Press, Oxford, 1966. Edited by a committee appointed by the London Mathematical Society. MR 0201267
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Robert S. Strichartz, A priori estimates for the wave equation and some applications, J. Functional Analysis 5 (1970), 218–235. MR 0257581, DOI 10.1016/0022-1236(70)90027-3
Additional Information
- Akos Magyar
- Affiliation: The Instittue for Advanced Study, Princeton, New Jersey 08540
- Address at time of publication: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 318009
- Email: amagyar@cco.caltech.edu
- Received by editor(s): September 28, 1995
- Communicated by: Christopher D. Sogge
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1969-1976
- MSC (1991): Primary 35L15; Secondary 11L07
- DOI: https://doi.org/10.1090/S0002-9939-97-03676-9
- MathSciNet review: 1363177