Journal of Convex Analysis 20 (2013), No. 3, 763--811
Copyright Heldermann Verlag 2013
Characterization of Uniformly Convex and Smooth Banach Spaces by Using Carleson Measures in Bessel Settings
Jorge J. Betancor
Dep. de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez s/n, 38271 La Laguna -- Sta. Cruz de Tenerife, Spain
jbetanco@ull.es
Alejandro J. Castro
Dep. de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez s/n, 38271 La Laguna -- Sta. Cruz de Tenerife, Spain
ajcastro@ull.es
Lourdes Rodríguez-Mesa
Dep. de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez s/n, 38271 La Laguna -- Sta. Cruz de Tenerife, Spain
lrguez@ull.es
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.
Keywords: BMO, Bessel operators, Carleson measures, uniformly convex, uniformly smooth, Banach spaces.
MSC: 46E40, 46B03, 42A50
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