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

Acta Mathematica Sinica, English Series volume 30, pages637–648(2014)Cite this article

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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Affiliations

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

    Alejandro J. Castro

  2. Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956, Warszawa, Poland

    Tomasz Z. Szarek

Authors
  1. Alejandro J. Castro
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  2. Tomasz Z. Szarek
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Corresponding author

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