Isomorphisms between spaces of Lipschitz functions

被引：10

作者：

Candido, Leandro ^{[1
]}

Cuth, Marek ^{[2
]}

Doucha, Michal ^{[3
]}

机构：

[1] Univ Fed Sao Paulo UNIFESP, Inst Ciencia & Tecnol, Dept Matemat, Av Cesare Monsueto Giulio Lattes 1201, BR-12247014 Sao Jose Dos Campos, SP, Brazil

[2] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 49-83, Prague 18675 8, Czech Republic

[3] Czech Acad Sci, Inst Math, Zitna 25, Prague 11567 1, Czech Republic

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2019年 / 277卷 / 08期

基金：

巴西圣保罗研究基金会;

关键词：

Lipschitz functions; Carnot groups; Lipschitz-free spaces; Orlicz spaces; SEPARATED NETS; PROPERTY; METRICS; THEOREM; GROWTH;

D O I：

10.1016/j.jfa.2019.02.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop tools for proving isomorphisms of normed spaces of Lipschitz functions over various doubling metric spaces and Banach spaces. In particular, we show that Lip(0)(Z(d)) similar or equal to_Lip(0)(R-d), for all d is an element of N. More generally, we e.g. show that Lip(0)(Gamma) similar or equal to Lip(0)(G), where Gamma is from a large class of finitely generated nilpotent groups and G is its Mal'cev closure; or that Lip(0)(l(p)) similar or equal to Lip(0)(L-p), for all 1 <= p <= infinity. We leave a large area for further possible research. (C) 2019 Published by Elsevier Inc.

引用

页码：2697 / 2727

页数：31

共 53 条

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