A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups
Functional Analysis
2022-06-06 v2 Metric Geometry
Abstract
We study the Lusin approximation problem for real-valued measurable functions on Carnot groups. We prove that k-approximate differentiability almost everywhere is equivalent to admitting a Lusin approximation by maps. We also prove that existence of an approximate (k-1)-Taylor polynomial almost everywhere is equivalent to admitting a Lusin approximation by maps in a suitable Lipschitz function space.
Cite
@article{arxiv.2107.12814,
title = {A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups},
author = {Marco Capolli and Andrea Pinamonti and Gareth Speight},
journal= {arXiv preprint arXiv:2107.12814},
year = {2022}
}
Comments
31 pages, updated with suggestions from referee