The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups

Vasileios Chousionis, Sean Li, Robert Young

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the β-numbers of intrinsic Lipschitz graphs of Heisenberg groups Hn are locally Carleson integrable when n≥2. Our main bound uses a novel slicing argument to decompose intrinsic Lipschitz graphs into graphs of Lipschitz functions. A key ingredient in our proof is a Euclidean inequality that bounds the β-numbers of the original graph in terms of the β-numbers of many families of slices. This allows us to use recent work of Fässler and Orponen (2020) which asserts that Lipschitz functions satisfy a Dorronsoro inequality.

Original languageEnglish (US)
Pages (from-to)251-274
Number of pages24
JournalJournal fur die Reine und Angewandte Mathematik
Volume2022
Issue number784
DOIs
StatePublished - Mar 1 2022

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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