Characterization of uniformly convex and smooth Banach spaces by using   Carleson measures in Bessel settings
  In this paper we obtain new characterizations of the q-uniformly convex and smooth Banach spaces by using Carleson measures. These measures are defined by Poisson integral associated with Bessel operators and Banach valued BMO-functions. By the way we describe q-uniformly convexity and smoothness of a Banach space in terms of the mapping properties of the Lusin integral defined by the Poisson semigroup for Bessel operators. 
Jorge J. Betancor, Alejandro J. Castro, Lourdes Rodr\'iguez-Mesa
math.CA