论文标题
Rademacher类型和ENFLO类型重合
Rademacher type and Enflo type coincide
论文作者
论文摘要
在ENFLO的古典作品中引入了Rademacher类型的非线性类似物。 ENFLO类型的关键特征是其定义仅使用Banach空间的度量结构，而Rademacher类型的定义依赖于其线性结构。我们证明了Rademacher类型和ENFLO类型是重合的，在Banach空间理论中解决了一个长期的开放问题。该证明是基于Pisier在离散立方体上的不平等现象的新颖无维度的类似物。
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.
