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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. |