$L^p$ Regularity Estimates for a Class of Integral Operators with Fold Blowdown Singularities
Classical Analysis and ODEs
2022-08-04 v2
Abstract
We prove sharp 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 estimates for related oscillatory integrals.
Keywords
Cite
@article{arxiv.2101.08233,
title = {$L^p$ Regularity Estimates for a Class of Integral Operators with Fold Blowdown Singularities},
author = {Geoffrey Bentsen},
journal= {arXiv preprint arXiv:2101.08233},
year = {2022}
}
Comments
31 pages. Reorganized the proof of Proposition 4. Revised version incorporating referee's suggestions. To appear in The Journal of Geometric Analysis