A1 Journal article (refereed)
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups (2022)

Di Donato, D., & Fässler, K. (2022). Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups. Annali di Matematica Pura ed Applicata, 201(1), 453-486. https://doi.org/10.1007/s10231-021-01124-3

JYU authors or editors

Publication details

All authors or editors: Di Donato, Daniela; Fässler, Katrin

Journal or series: Annali di Matematica Pura ed Applicata

ISSN: 0373-3114

eISSN: 1618-1891

Publication year: 2022

Publication date: 07/06/2021

Volume: 201

Issue number: 1

Pages range: 453-486

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s10231-021-01124-3

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/76357

Publication is parallel published: https://arxiv.org/abs/2012.12609

Abstract

This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group Hn, n∈N. For 1⩽k⩽n, we show that every intrinsic L-Lipschitz graph over a subset of a k-dimensional horizontal subgroup V of Hn can be extended to an intrinsic L′-Lipschitz graph over the entire subgroup V, where L′ depends only on L, k, and n. We further prove that 1-dimensional intrinsic 1-Lipschitz graphs in Hn, n∈N, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that were known previously only in the first Heisenberg group H1. The main difference to this case arises from the fact that for 1⩽k

Keywords: mathematical analysis; measure theory

Free keywords: Heisenberg groups; Lipschitz extension; corona decomposition; low-dimensional intrinsic Lipschitz graphs

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Ministry reporting: Yes

VIRTA submission year: 2022

JUFO rating: 1