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 editorsDi Donato, Daniela; Fässler, Katrin

Journal or seriesAnnali di Matematica Pura ed Applicata



Publication year2022

Publication date07/06/2021


Issue number1

Pages range453-486


Publication countryGermany

Publication languageEnglish


Publication open accessOpenly available

Publication channel open accessPartially open access channel

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

Publication is parallel publishedhttps://arxiv.org/abs/2012.12609


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

Keywordsmathematical analysismeasure theory

Free keywordsHeisenberg groups; Lipschitz extension; corona decomposition; low-dimensional intrinsic Lipschitz graphs

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Ministry reportingYes

Reporting Year2022

JUFO rating1

Last updated on 2024-15-06 at 00:26