Fractal Strichartz estimate for the wave equation

TL;DR

This paper establishes new Strichartz estimates for the wave equation with respect to general measures, achieving sharp results in four dimensions and improvements in higher dimensions, advancing the understanding of wave behavior under measure-based conditions.

Contribution

The paper introduces novel Strichartz estimates for the wave equation with general measures, providing sharp results in 3+1 dimensions and enhancements over previous bounds in higher dimensions.

Findings

Achieved sharp Strichartz estimates in 3+1 dimensions.

Improved existing estimates in higher dimensions.

Extended the applicability of Strichartz estimates to general measures.

Abstract

We consider Strichartz estimates for the wave equation with respect to general measures which satisfy certain growth condition. In $\mathbb R^{3+1}$ we obtain the sharp estimate and in higher dimensions improve the previous results.