On Oscillatory Integral Operators Satisfying the cinematic curvature condition

TL;DR

This paper proves near-optimal L^r to L^p bounds for a class of oscillatory integral operators under the cinematic curvature condition, using advanced techniques like decoupling and two-ends reduction.

Contribution

It introduces a nearly sharp estimate for oscillatory integral operators satisfying the cinematic curvature condition, combining Wolff's reduction with refined decoupling methods.

Findings

Established almost sharp L^r to L^p bounds

Combined Wolff's two-ends reduction with decoupling inequalities

Enhanced understanding of oscillatory integral operators under curvature conditions

Abstract

We establish an almost sharp L^r to L^p estimate for oscillatory integral operators satisfying the cinematic curvature condition. The proof combines Wolff's two-ends reduction with refined decoupling inequalities.