On space-time estimates for the Schroedinger operator

TL;DR

This paper establishes mixed norm space-time estimates for solutions to the Schrödinger equation with initial data in various function spaces, enhancing understanding of their behavior and connections to restriction phenomena.

Contribution

It provides new mixed norm estimates for Schrödinger solutions and clarifies their relation to adjoint restriction, advancing the theoretical framework.

Findings

Derived space-time estimates for Schrödinger solutions.

Connected estimates to adjoint restriction theory.

Extended results to initial data in Sobolev and Besov spaces.

Abstract

We prove mixed norm space-time estimates for solutions of the Schroedinger equation, with initial data in $L^p$ Sobolev or Besov spaces, and clarify the relation with adjoint restriction.