Strichartz Estimates for Non-selfadjoint Operators and Applications

Abstract

We prove Strichartz type estimates for non-selfadjoint pseudo-differential operators of order m with a curvature condition on the characteristic set. Local solvability results for the corresponding equations with L n/m potential (where n > m stands for the number of variables) and for the corresponding semi-linear equations with a non-linearity of order m/n ≤ α ≤ 2m/(n − m) follow. This is achieved using a parametrix construction and a Brenner inequality for Fourier integral operators with complex phase.