Dorronsoro's theorem in Heisenberg groups
Copyright policy )Dorronsoro's theorem in Heisenberg groups
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
- University of Helsinki Finland
- University of Fribourg Switzerland
- University of Jyväskylä Finland
- RERO - Library Network of Western Switzerland Switzerland
Dorronsoro's theorem, Heisenberg groups, ta111, Metric Geometry (math.MG), harmoninen analyysi, matemaattinen analyysi, 26B05 (Primary) 26A33, 42B35 (Secondary), Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, horizontal Sobolev spaces, approximation by affine functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, info:eu-repo/classification/udc/51, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Function spaces arising in harmonic analysis
Dorronsoro's theorem, Heisenberg groups, ta111, Metric Geometry (math.MG), harmoninen analyysi, matemaattinen analyysi, 26B05 (Primary) 26A33, 42B35 (Secondary), Mathematics - Metric Geometry, Mathematics - Classical Analysis and ODEs, horizontal Sobolev spaces, approximation by affine functions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, info:eu-repo/classification/udc/51, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, Function spaces arising in harmonic analysis
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