paper

Strong hypercontractivity in non-commutative holomorphic spaces

arXiv:math/0410534 · doi:10.1007/s00220-005-1379-5

Abstract

We introduce holomorphic algebras $H_q$ in the context of the q-Gaussian algebra $Î_q$ of Bozejko, KÃ¼mmerer, and Speicher, and give a q-Segal-Bargmann transform for them. We then prove a strong hypercontractivity theorem, generalizing Janson's strong (holomorphic) hypercontractivity, from $L^2(H_q) \to L^r(H_q)$ for r an even integer.

25 pages, uses package xy