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 An�lisis Matem�tico, Universidad de la Laguna, Campus de Anchieta, Avda. Astrof�sico Francisco S�nchez s/n, 38271 La Laguna -- Sta. Cruz de Tenerife, Spain
jbetanco@ull.es
Alejandro J. Castro
Dep. de An�lisis Matem�tico, Universidad de la Laguna, Campus de Anchieta, Avda. Astrof�sico Francisco S�nchez s/n, 38271 La Laguna -- Sta. Cruz de Tenerife, Spain
ajcastro@ull.es
Lourdes Rodr�guez-Mesa
Dep. de An�lisis Matem�tico, Universidad de la Laguna, Campus de Anchieta, Avda. Astrof�sico Francisco S�nchez 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
[ Fulltext-pdf (328 KB)] for subscribers only.