Sharp Strichartz estimates in spherical coordinates

TL;DR

This paper establishes sharp Strichartz estimates for Schrödinger-like equations in spherical coordinates, enhancing understanding of regularity effects and providing near-optimal bounds through spherical averaging techniques.

Contribution

It introduces almost Strichartz estimates with added regularity in spherical coordinates, achieving sharpness up to endpoint cases and employing spherical average estimates.

Findings

Establishes sharp almost Strichartz estimates in spherical coordinates.

Demonstrates the estimates are sharp up to endpoint cases.

Uses spherical averages and Knapp-type examples to analyze sharpness.

Abstract

We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness is discussed making use of a modified Knapp-type example.