Lp Regularity Estimates for a Class of Integral Operators with Fold Blowdown Singularities

Geoffrey Bentsen

doi:10.1007/s12220-021-00791-1

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

Geoffrey Bentsen^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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 L² estimates for related oscillatory integrals.

Original language	English (US)
Article number	89
Journal	Journal of Geometric Analysis
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s12220-021-00791-1
State	Published - Mar 2022

Keywords

Fourier integral operators
Radon transforms
Regularity of integral operators
X-ray transforms

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s12220-021-00791-1

Cite this

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title = "Lp Regularity Estimates for a Class of Integral Operators with Fold Blowdown Singularities",

abstract = "We prove sharp Lp 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 L2 estimates for related oscillatory integrals.",

keywords = "Fourier integral operators, Radon transforms, Regularity of integral operators, X-ray transforms",

author = "Geoffrey Bentsen",

note = "Funding Information: Research supported in part by NSF Grant DMS 1764295. Publisher Copyright: {\textcopyright} 2021, Mathematica Josephina, Inc.",

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AB - We prove sharp Lp 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 L2 estimates for related oscillatory integrals.

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KW - Regularity of integral operators

KW - X-ray transforms

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