PreprintarXiv licencearXiv
Rademacher Type and Enflo Type Revisited
Abstract
We establish a dimension-free vector-valued Poincaré-type inequality on the discrete cube for Banach spaces with Rademacher type p, 1≤ p≤2. As a consequence, we obtain TpR(X)≤ TpE(X)≤ p TpR(X). This gives an alternative proof that Rademacher type and Enflo type coincide, while improving the constant π/√2 in the quantitative estimate of Ivanisvili, van Handel, and Volberg \cite{IVV} to p.
Related
- The Rademacher quotient of L1 embeds into L1 and its weak Calkin algebra is uniformly incompressible
- Large fluctuations of extended Rademacher random multiplicative functions
- High-Arity Rademacher Complexity and Uniform Laws of Large Numbers
- Low moments of sums of extended Rademacher random multiplicative functions
- Sharp p/log p Bounds for Metric Xp Inequalities and Arbitrary Rademacher Chaos
BibTeX
@misc{areshidze2026rademacher,
title = {{Rademacher Type and Enflo Type Revisited}},
author = {Nika Areshidze},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32666},
eprint = {2609.32666},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32666},
}
RIS
TY - UNPB
TI - Rademacher Type and Enflo Type Revisited
AU - Nika Areshidze
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32666
UR - https://arxiv.org/abs/2609.32666
AB - We establish a dimension-free vector-valued Poincaré-type inequality on the discrete cube for Banach spaces with Rademacher type p, 1≤ p≤2. As a consequence, we obtain T_p^R(X)≤ T_p^E(X)≤ p T_p^R(X). This gives an alternative proof that Rademacher type and Enflo type coincide, while improving the constant π/√2 in the quantitative estimate of Ivanisvili, van Handel, and Volberg \cite{IVV} to p.
ER -