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

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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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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Mathematics Subject Classification

  • Primary 46E40
  • 42B25
  • Secondary 42A50
  • 42B35

Keywords

  • Square functions
  • Bessel operators
  • UMD spaces
  • Hardy
  • BMO