arXiv subjects

Geoffrey Bentsen

Publications and source records attributed to Geoffrey Bentsen.

2 recordsLinked to original sources

arXiv2021

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

We prove sharp $L^p$ 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 $L^2$ estimates for related oscillatory integrals.

math.CA↗

arXiv2020

$L^p$ regularity for a class of averaging operators on the Heisenberg group

We prove $L^p_{comp}\to L^p_{s}$ boundedness for averaging operators associated to a class of curves in the Heisenberg group $\mathbb{H}^1$ via $L^2$ estimates for related oscillatory integrals and Bourgain-Demeter decoupling inequalities on the cone. We also construct a Sobolev space adapted to translations on the Heisenberg group to which these averaging operators map all $L^p$ functions boundedly.

math.CA↗