$L^p$ 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 to 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.

31 pages. Reorganized the proof of Proposition 4. Revised version incorporating referee's suggestions. To appear in The Journal of Geometric Analysis

References in corpus (3)

• Compactness Properties of Weighted Summation Operators on Trees
• Optimal regularity of Fourier integral operators with one-sided folds
• $L^p$ regularity for a class of averaging operators on the Heisenberg group

Cited by in corpus (2)

• Sharp Sobolev regularity of restricted X-ray transforms
• Sharp smoothing properties of averages over curves