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

Geoffrey Bentsen

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

Classical Analysis and ODEs 2022-08-04 v2

Authors: Geoffrey Bentsen

Abstract

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.

Keywords

heisenberg group averaging operators l^p boundedness oscillatory integrals decoupling inequalities sobolev space

Cite

@article{arxiv.2002.01917,
  title  = {$L^p$ regularity for a class of averaging operators on the Heisenberg group},
  author = {Geoffrey Bentsen},
  journal= {arXiv preprint arXiv:2002.01917},
  year   = {2022}
}

Comments

32 pages, 2 figures. Added references, added detail to proof of Corollary 1.1, result unchanged. Made additional changes reflecting anonymous referee's comments

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

Abstract

Keywords

Cite

Comments

Related papers