Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {L}}^{{\mathbf {p}}}$$\end{document}-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations

We prove a sharp Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-Sobolev regularity result 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.