$L^p$-Sobolev estimates for a class of integral operators with folding canonical relations

TL;DR

This paper establishes sharp $L^p$-Sobolev regularity estimates for certain integral operators with folding canonical relations, using advanced decoupling inequalities in a three-dimensional setting.

Contribution

It introduces new sharp regularity results for generalized Radon transforms with folding canonical relations in three dimensions.

Findings

Proves sharp $L^p$-Sobolev estimates for a class of integral operators.

Utilizes decoupling inequalities by Wolff and Bourgain-Demeter.

Extends understanding of Radon transforms with folding canonical relations.

Abstract

We prove a sharp $L^p$-Sobolev regularity results for a class of generalized Radon transforms for families of curves in a three dimensional manifold, with folding canonical relations. The proof relies on decoupling inequalities by Wolff and by Bourgain-Demeter for plate decompositions of thin neighborhoods of cones.