Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • BMO
  • Bessel operators
  • Carleson measures
  • uniformly convex
  • uniformly smooth
  • Banach spaces

Mathematics Subject Classification

46E40, 46B03, 42A50

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Suggested citation

J. J. Betancor, A. J. Castro, L. Rodríguez-Mesa. “Characterization of Uniformly Convex and Smooth Banach Spaces by Using Carleson Measures in Bessel Settings.” Journal of Convex Analysis 20 (2013), No. 3, 763–811. https://doi.org/10.68381/jca20043

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.