Strichartz type Inequalities for Parabolic and Schr\"odinger Equations in rearrangement invariant Spaces

TL;DR

This paper extends classical Strichartz inequalities to solutions of linear parabolic and Schrödinger equations within various rearrangement invariant spaces, providing generalized estimates and demonstrating their optimality through examples.

Contribution

It introduces generalized Strichartz estimates for linear PDEs in rearrangement invariant spaces and proves their sharpness with explicit examples.

Findings

Generalized Strichartz inequalities for parabolic and Schrödinger equations.

Construction of examples showing the exactness of the estimates.

Extension of classical results to a broader class of function spaces.

Abstract

In this paper we generalize the classical Strichartz estimation for solutions of initial problem for linear parabolic and Schr\"odinger PDE on many popular classes {\it pairs} of rearrangement invariant(r.i.) spaces and construct some examples in order to show the exactness of our estimations.