Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Andrea Pinamonti , Gareth Speight , Scott Zimmerman
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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.

海森堡群中水平曲线的高阶惠特尼扩展和卢辛近似
在海森堡群水平曲线的背景下,我们证明了 Cm,ω 有限性原理、Cm,ω Lusin 近似结果、C∞ 惠特尼扩展结果和 C∞ Lusin 近似结果。结合之前的工作,这完成了对海森堡群中 Cm、Cm,ω 和 C∞ 类水平曲线的惠特尼扩展和卢辛近似的研究。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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