Calderón-Zygmund operators in the Bessel setting for all possible type indices

Abstract

We show that many harmonic analysis operators in the Bessel setting, including maximal operators, Littlewood-Paley-Stein type square functions, multipliers of Laplace or Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as, Calderón-Zygmund operators for all possible values of type parameter λ in this context. This extends results existing in the literature, but being justified only for a restricted range of λ.

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Correspondence to Tomasz Z. Szarek.

Additional information

The first author is supported by MTM2010/17974 and an FPU Grant from the Government of Spain

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Castro, A.J., Szarek, T.Z. Calderón-Zygmund operators in the Bessel setting for all possible type indices. Acta. Math. Sin.-English Ser. 30, 637–648 (2014). https://doi.org/10.1007/s10114-014-2326-1

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Keywords

  • Bessel operator
  • Bessel semigroup
  • maximal operator
  • square function
  • multiplier
  • Riesz transform
  • Calderón-Zygmund operator

MR(2010) Subject Classification

  • 42C05
  • 42B20