A Ck Lusin Approximation Theorem for Real-Valued Functions on Carnot Groups

被引：0

作者：

Capolli, Marco ^{[1
]}

Pinamonti, Andrea ^{[2
]}

Speight, Gareth ^{[3
]}

机构：

[1] Polish Acad Sci Warsaw, Inst Math, Jana & Jadrzeja Sniadeckich 8, PL-00656 Warsaw, Poland

[2] Univ Trento, Math Dept, Via Sommar 14, I-38123 Povo, Trento, Italy

[3] Univ Cincinnati, Dept Math Sci, 2815 Commons Way, Cincinnati, OH 45221 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2023年 / 72卷 / 04期

关键词：

WHITNEY EXTENSION THEOREM; HORIZONTAL CURVES; HIGHER-ORDER; DIFFERENTIABILITY; PROPERTY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Lusin approximation problem for real-valued measurable functions on Carnot groups. We prove that k-approximate differentiability almost everywhere is equiv-alent to admitting a Lusin approximation by CGk maps. We also prove that existence of an approximate (k - 1)-Taylor polyno-mial almost everywhere is equivalent to admitting Lusin approx-imation by maps in a suitable Lipschitz function space.

引用

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页码：1327 / 1365

页数：39

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