Dorronsoro’s theorem in Heisenberg groups

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
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

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Mathematics

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https://folia.unifr.ch/unifr/documents/308722
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