Year: 2026
Type: preprint
Abstract: We establish a dimension-free vector-valued Poincaré-type inequality on the discrete cube for Banach spaces with Rademacher type $p$, $1\le p\le2$. As a consequence, we obtain $$ T_p^R(X)\le T_p^E(X)\le p\,T_p^R(X). $$ This gives an alternative proof that Rademacher type and Enflo type coincide, while improving the constant $π/\sqrt{2}$ in the quantitative estimate of Ivanisvili, van Handel, and Volberg \cite{IVV} to $p$.
Source: arXiv (Cornell University)
Author: Areshidze, Nika
Institution: University of California, Irvine
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214806399