Dorronsoro’s theorem in Heisenberg groups

Fässler, Katrin; Orponen, Tuomas

doi:10.1112/blms.12341

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Journal article

Dorronsoro’s theorem in Heisenberg groups

Université de Fribourg

Fässler, Katrin Department of Mathematics, University of Fribourg, Chemin du Musée 23 Fribourg CH‐1700 Switzerland - Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä FI‐40014 Finland
Orponen, Tuomas Department of Mathematics and Statistics, University of Helsinki, Helsinki FI‐00014 Finland

2020

Published in:

Bulletin of the London Mathematical Society. - 2020, vol. 52, no. 3, p. 472–488

English 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 versus horizontal Poincaré inequalities for real‐valued functions on the Heisenberg group, originally due to Austin–Naor–Tessera and Lafforgue–Naor.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language