Rademacher type and Enflo type coincide
成果类型：
Article
署名作者：
Ivanisvili, Paata; van Handel, Ramon; Volberg, Alexander
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2020.192.2.8
发表日期：
2020
页码：
665-678
关键词：
摘要：
A nonlinear analogue of the Rademacher type of a Banach space was introduced in classical work of Enflo. The key feature of Enflo type is that its definition uses only the metric structure of the Banach space, while the definition of Rademacher type relies on its linear structure. We prove that Rademacher type and Enflo type coincide, settling a long-standing open problem in Banach space theory. The proof is based on a novel dimension-free analogue of Pisier's inequality on the discrete cube.