Isomorphisms between spaces of Lipschitz functions

Author(s)

Candido, Leandro ^[1] ; Cuth, Marek ^[2] ; Doucha, Michal ^[3]

Affiliation

^[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

• Document type: Journal article
• Source: JOURNAL OF FUNCTIONAL ANALYSIS; v. 277, n. 8, p. 2697-2727, OCT 15 2019.
• Web of Science Citations: 0

Abstract

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. (AU)

• FAPESP's process: 16/25574-8 - Geometry of Banach Spaces
• Grantee: Valentin Raphael Henri Ferenczi
• Support Opportunities: Research Projects - Thematic Grants