Global Range Estimates for Maximal Oscillatory Integrals with Radial Testfunctions

TL;DR

This paper establishes near-sharp global estimates for the maximal function of oscillatory integrals when applied to radial test functions, advancing understanding of their regularity properties.

Contribution

It provides the first near-sharp global bounds for oscillatory integral maximal functions specifically for radial test functions.

Findings

Achieved near-sharp Sobolev regularity estimates

Extended the understanding of oscillatory integral maximal functions

Focused on radial test functions for precise bounds

Abstract

We consider the maximal function of oscillatory integrals and prove a global estimate for radial test functions which is almost sharp with respect to the Sobolev regularity.