On weighted 𝐿² estimates for solutions of the wave equation

Koh, Youngwoo; Seo, Ihyeok

doi:10.1090/proc/12951

On weighted $L^2$ estimates for solutions of the wave equation
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by Youngwoo Koh and Ihyeok Seo PDF

Proc. Amer. Math. Soc. 144 (2016), 3047-3061 Request permission

Abstract:

In this paper we consider weighted $L^2$ integrability for solutions of the wave equation. For this, we obtain some weighed $L^2$ estimates for the solutions with weights in Morrey-Campanato classes. Our method is based on a combination of bilinear interpolation and a localization argument which makes use of the Littlewood-Paley theorem and a property of Hardy-Littlewood maximal functions. We also apply the estimates to the problem of well-posedness for wave equations with potentials.

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