In the setting of horizontal curves in the Heisenberg group, we prove a Cm,ω finiteness principle, a Cm,ω Lusin approximation result, a C∞ Whitney extension result, and a C∞ Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class Cm, Cm,ω, and C∞ in the Heisenberg group.
Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group / Pinamonti, Andrea; Speight, Gareth; Zimmerman, Scott. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 2024, 188:(2024), pp. 320-344. [10.1016/j.matpur.2024.06.005]
Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group
Pinamonti, Andrea
;Speight, Gareth;
2024-01-01
Abstract
In the setting of horizontal curves in the Heisenberg group, we prove a Cm,ω finiteness principle, a Cm,ω Lusin approximation result, a C∞ Whitney extension result, and a C∞ Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class Cm, Cm,ω, and C∞ in the Heisenberg group.| File | Dimensione | Formato | |
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