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UMD-Valued Square Functions Associated with Bessel Operators in Hardy and BMO Spaces

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Abstract

We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If \({\mathbb{B}}\) is a UMD Banach space we obtain for \({\mathbb{B}}\) -valued Hardy and BMO spaces equivalent norms involving γ-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by means of Hardy and BMO-boundedness properties of g-functions associated to Bessel–Poisson semigroup.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de La Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271, La Laguna, Santa Cruz de Tenerife, Spain

    Jorge J. Betancor & Lourdes Rodríguez-Mesa

  2. Department of Mathematics, Uppsala University, S-751 06, Uppsala, Sweden

    Alejandro J. Castro

Authors
  1. Jorge J. Betancor
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  2. Alejandro J. Castro
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  3. Lourdes Rodríguez-Mesa
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Correspondence to Lourdes Rodríguez-Mesa.

Additional information

J. J. Betancor, A. J. Castro and L. Rodríguez-Mesa were partially supported by MTM2010/17974. A. J. Castro was also supported by a FPU grant from the Government of Spain.

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Betancor, J.J., Castro, A.J. & Rodríguez-Mesa, L. UMD-Valued Square Functions Associated with Bessel Operators in Hardy and BMO Spaces. Integr. Equ. Oper. Theory 81, 319–374 (2015). https://doi.org/10.1007/s00020-014-2202-5

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  • DOI: https://doi.org/10.1007/s00020-014-2202-5

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