WHITNEY-TYPE EXTENSIONS IN QUASI-METRIC SPACES

被引：5

作者：

Alvarado, Ryan ^{[1
]}

Mitrea, Irina ^{[2
]}

Mitrea, Marius ^{[1
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2013年 / 12卷 / 01期

基金：

美国国家科学基金会;

关键词：

Quasi-metric space; geometrically doubling quasi-metric space; extension of Holder functions; extension of Lipschitz functions; quasi-metric space; metrization; Holder functions; Lipschitz functions; partition of unity; Whitney extension; quantitative Urysohn lemma; Whitney decomposition;

D O I：

10.3934/cpaa.2013.12.59

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss geometrical scenarios guaranteeing that functions defined on a given set may be extended to the entire ambient, with preservation of the class of regularity. This extends to arbitrary quasi-metric spaces work done by E.J. McShane in the context of metric spaces, and to geometrically doubling quasi-metric spaces work done by H. Whitney in the Euclidean setting. These generalizations are quantitatively sharp.

引用

页码：59 / 88

页数：30

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