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
Contributing organizations
Related projects
- Singular integrals, harmonic functions and boundary regularity in Heisenberg groups
- Fässler, Katrin
- Research Council of Finland
Ministry reporting: Yes
VIRTA submission year: 2022
JUFO rating: 1