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

Abstract

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

29 pages

References in corpus (3)

• Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi
• $\gamma$-Radonifying operators -- a survey
• Vector-valued Littewood-Paley-Stein theory for semigroups II

Cited by in corpus (1)

• UMD Banach spaces and the maximal regularity for the square root of several operators