Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
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
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202106083571Use this for linking
Review status
Peer reviewed
ISSN
0373-3114
DOI
https://doi.org/10.1007/s10231-021-01124-3
Language
English
Published in
Annali di Matematica Pura ed Applicata
Citation
- 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
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Funder(s)
Research Council of Finland
Funding program(s)
Academy Research Fellow, AoF
Akatemiatutkija, SA
Additional information about funding
Open access funding provided by Scuola Internazionale Superiore di Studi Avanzati - SISSA within the CRUI-CARE Agreement.
Copyright© 2021 the Authors