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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the almost everywhere convergence to $ L\sp p$ data for higher order hyperbolic operators


Author: Christopher D. Sogge
Journal: Proc. Amer. Math. Soc. 100 (1987), 99-103
MSC: Primary 35L15; Secondary 42B25
MathSciNet review: 883408
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Abstract: First we prove a sharp maximal Fourier integral theorem for $ {L^p}({{\mathbf{R}}^n}),\;1 < p \leq 2$, using the techniques of [4-6]. Then we apply the maximal theorem to prove a sharp result concerning the almost everywhere convergence to $ {L^p}$-initial data for the Cauchy problem for smooth variable coefficient strictly hyperbolic linear partial differential operators of order $ m > 2$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0883408-3
PII: S 0002-9939(1987)0883408-3
Article copyright: © Copyright 1987 American Mathematical Society