Generalized and weighted Strichartz estimates. (English) Zbl 1264.35011
Summary: We explore the relations between different kinds of Strichartz estimates and give new estimates in Euclidean space \(\mathbb R^n\). 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 \(3\).
MSC:
35A23 | Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals |
35L71 | Second-order semilinear hyperbolic equations |
35B45 | A priori estimates in context of PDEs |