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Dorronsoro's theorem in Heisenberg groups

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 22 May 2020Embargo end date: 01 Jan 2019 Switzerland Publisher:WileyJournal:Bulletin of the London Mathematical Society, volume 52, pages 472-488 (issn: 0024-6093, eissn: 1469-2120,

Authors: Orponen; Tuomas; Fässler, Katrin;

doi: 10.1112/blms.12341 , 10.48550/arxiv.1901.04767

arXiv: http://arxiv.org/abs/1901.04767

Dorronsoro's theorem in Heisenberg groups

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Abstract

A theorem of Dorronsoro from the 1980s quantifies the fact that real-valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theorem in Heisenberg groups: functions in horizontal Sobolev spaces can be approximated by affine functions which are independent of the last variable. As an application, we deduce new proofs for certain vertical vs. horizontal Poincar�� inequalities for real-valued functions on the Heisenberg group, originally due to Austin-Naor-Tessera and Lafforgue-Naor.

16 pages

Country

Switzerland

Related Organizations

University of Helsinki
Finland
University of Jyväskylä
Finland
University of Fribourg
Switzerland
RERO - Library Network of Western Switzerland
Switzerland

Keywords

26B05 (Primary) 26A33, 42B35 (Secondary), Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, ta111, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Metric Geometry (math.MG), harmoninen analyysi, matemaattinen analyysi

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