$$L^p$$ Regularity Estimates for a Class of Integral Operators with Fold Blowdown Singularities

Abstract

We prove sharp \(L^p\) regularity results for a class of generalized Radon transforms for families of curves in a three-dimensional manifold associated with a canonical relation with fold and blowdown singularities. The proof relies on decoupling inequalities by Wolff and Bourgain–Demeter for plate decompositions of thin neighborhoods of cones and \(L^2\) estimates for related oscillatory integrals.