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Dorronsoro's theorem in Heisenberg groups
Katrin FässlerKatrin FässlerTuomas Orponensubject
Pure mathematicsGeneral Mathematics010102 general mathematicsMathematical proof01 natural sciencesSobolev spacesymbols.namesakeEuclidean geometryPoincaré conjectureHeisenberg groupsymbolsAlmost everywhereAffine transformation0101 mathematicsVariable (mathematics)Mathematicsdescription
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 Poincare inequalities for real-valued functions on the Heisenberg group, originally due to Austin-Naor-Tessera and Lafforgue-Naor.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-05-22 | Bulletin of the London Mathematical Society |