Lp Regularity for a Class of Averaging Operators on the Heisenberg Group

Geoffrey Bentsen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We prove Lpcomp(R3) → Lps (R3) boundedness for averaging operators associated with a class of curves in the Heisenberg group H1 via L2 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 Lp functions boundedly.

Original languageEnglish (US)
Pages (from-to)819-855
Number of pages37
JournalIndiana University Mathematics Journal
Volume71
Issue number5
DOIs
StatePublished - 2022

Funding

This research been supported in part by the National Science Foundation (grant no. DMS 1764295).

ASJC Scopus subject areas

  • General Mathematics

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