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arXiv · 2107.12814

A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups

Marco Capolli·Andrea Pinamonti·Gareth Speight
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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 $C^{k}_{\mathbb{G}}$ 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.

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Marco Capolli, Andrea Pinamonti, Gareth Speight. 2021-07-27. A C^k Lusin Approximation Theorem For Real-Valued Functions on Carnot Groups. https://arxiv.org/abs/2107.12814

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