Calderón-Zygmund operators in the Bessel setting

Abstract

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calderón-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.

21 pages

References in corpus (2)

• Hankel Multipliers of Laplace Transform Type
• Harmonic Analysis Operators Associated with Multidimensional Bessel Operators

Cited by in corpus (12)

• Calderón-Zygmund operators in the Bessel setting for all possible type indices
• On fundamental harmonic analysis operators in certain Dunkl and Bessel settings
• Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework
• On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
• On pointwise ${\ell }^r$-sparse domination in a space of homogeneous type
• Potential operators associated with Hankel and Hankel-Dunkl transforms
• $L^p$-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators
• Riesz transform characterizations for multidimensional Hardy spaces
• Bellman Functions and Dimension Free $L^p$estimates for the Riesz Transforms in Bessel settings
• Multipliers of Laplace transform type in certain Dunkl and Laguerre settings
• Sharp multiplier theorem for multidimensional Bessel operators
• Endpoint bounds of square functions associated with Hankel multipliers