$${\mathbf {L}}^{{\mathbf {p}}}$$-Sobolev Estimates for a Class of Integral Operators 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.