Higher order Whitney extension and Lusin approximation for Horizontal curves in the Heisenberg group Article Swipe
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Heisenberg group
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Andrea Pinamonti
,
Gareth Speight
,
Scott Zimmerman
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2310.06953
· OA: W4387595864
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2310.06953
· OA: W4387595864
In the setting of horizontal curves in the Heisenberg group, we prove a $C^{m,ω}$ finiteness principle, a $C^{m,ω}$ Lusin approximation result, a $C^{\infty}$ Whitney extension result, and a $C^{\infty}$ Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class $C^{m}$, $C^{m,ω}$, and $C^{\infty}$ in the Heisenberg group.
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