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Positivity

, Volume 17, Issue 3, pp 535–587 | Cite as

Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions

  • Jorge J. Betancor
  • Alejandro J. Castro
  • Lourdes Rodríguez-Mesa
Article
  • 125 Downloads

Abstract

In this paper we consider the space \({{{BMO}_o(\mathbb{R}, X)}}\) of bounded mean oscillations and odd functions on \({{\mathbb{R}}}\) taking values in a UMD Banach space X. The functions in \({{{BMO}_o(\mathbb{R}, X)}}\) are characterized by Carleson type conditions involving Bessel convolutions and γ-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain γ-radonifying Carleson inequalities for Bessel–Poisson integrals of \({{{BMO}_o(\mathbb{R}, X)}}\) functions hold.

Keywords

γ-Radonifying operators BMO Bessel convolution UMD Banach spaces 

Mathematics Subject Classification (2010)

46E40 42A50 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Jorge J. Betancor
    • 1
  • Alejandro J. Castro
    • 1
  • Lourdes Rodríguez-Mesa
    • 1
  1. 1.Departamento de Análisis MatemáticoUniversidad de La LagunaLa LagunaSpain

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