$L^p$-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.

To appear in Journal of Geometric Analysis

References in corpus (4)

• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds
• Compactness Properties of Weighted Summation Operators on Trees
• Optimal regularity of Fourier integral operators with one-sided folds
• Spherical means on the Heisenberg group: Stability of a maximal function estimate

Cited by in corpus (2)

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