L p′ –L p decay estimates of solutions to the wave equation with a short-range potential

Abstract

We obtain large time decay of the L^p norms, 2<p<+∞, of solutions to the wave equation with a real-valued potential which decays slowly at infinity. This extends previous results by Beals and Strauss [Comm. Partial Differential Equations 18 (1993), 1365–1397] and Georgiev and Visciglia [Comm. Partial Differential Equations 28 (2003), 1325–1369].