Rademacher type and Enflo type coincide
Rademacher type and Enflo type coincide
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DOI：
10.4007/annals.2020.192.2.8
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发表时间：
2020-03
影响因子：
4.9
通讯作者：
P. Ivanisvili;R. Handel;A. Volberg
中科院分区：
文献类型：
--
作者：
P. Ivanisvili;R. Handel;A. Volberg
一个非线性模拟的Rademacher型的Banach空间中介绍了经典工作的Enflo。Enflo型的主要特点是它的定义只使用Banach空间的度量结构，而Rademacher型的定义依赖于它的线性结构。我们证明了Rademacher型与Enflo型是一致的，解决了Banach空间理论中一个长期存在的问题。证明是基于一个新的无量纲模拟的离散立方体上的皮西尔不等式。
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.