Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions

摘要

In this paper we consider the space ({{{BMO}_o(mathbb{R}, X)}}) of bounded mean oscillations and odd functions on ({{mathbb{R}}}) taking values in a UMD Banach space X. The functions in ({{{BMO}_o(mathbb{R}, X)}}) are characterized by Carleson type conditions involving Bessel convolutions and γ-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain γ-radonifying Carleson inequalities for Bessel–Poisson integrals of ({{{BMO}_o(mathbb{R}, X)}}) functions hold.