Generalized and weighted strichartz estimates

Abstract

In this paper, we explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space ℝn. In particular, we prove the generalized and weighted Strichartz estimates for a large class of dispersive operators including the Schrödinger and wave equation. As a sample application of these new estimates, we are able to prove the Strauss conjecture with low regularity for dimension 2 and 3.