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

Geoffrey Bentsen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Article number89
JournalJournal of Geometric Analysis
Volume32
Issue number3
DOIs
StatePublished - Mar 2022

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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