On weighted $L^2$ estimates for solutions of the wave equation

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 localization argument which makes use of 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.

To appear in Proc. Amer. Math. Soc., 15 pages

References in corpus (1)

• From resolvent estimates to unique continuation for the Schrödinger equation

Cited by in corpus (2)

• Global well-posedness for higher-order Schrödinger equations in weighted $L^2$ spaces
• Strichartz estimates for Schrödinger equations in weighted $L^2$ spaces and their applications