On the almost everywhere convergence to 𝐿^{𝑝} data for higher order hyperbolic operators

Sogge, Christopher D.

doi:10.1090/S0002-9939-1987-0883408-3

On the almost everywhere convergence to $L^ p$ data for higher order hyperbolic operators
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by Christopher D. Sogge

Proc. Amer. Math. Soc. 100 (1987), 99-103

DOI: https://doi.org/10.1090/S0002-9939-1987-0883408-3

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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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