WHITNEY-TYPE EXTENSIONS IN QUASI-METRIC SPACES

被引：6

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

共 31 条

[1]

[Anonymous], 1943, Bull. Am. Math. Soc, DOI DOI 10.1090/S0002-9904-1943-07859-7

[2]

[Anonymous], 1971, Lecture Notes in Mathematics

[3]

[Anonymous], 1970, SINGULAR INTEGRALS D

[4]

[Anonymous], 1958, Ark. Mat., DOI 10.1007/BF02589517

[5]

Aoki T., 1942, P IMP ACAD TOKYO, V18, P588, DOI DOI 10.3792/PIA/1195573733

[6] Whitney's extension problem for multivariate C1,w-functions [J].

Brudnyi, Y ;

Shvartsman, P .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (06) :2487-2512

[7]

Chen L., ARXIV10103299V1

[8]

Chen L., ARXIV10053727V1

[9] EXTENSIONS OF HARDY SPACES AND THEIR USE IN ANALYSIS [J].

COIFMAN, RR ;

WEISS, G .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 83 (04) :569-645

[10]

Engelking R., 1989, General topology

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