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) Calderon–Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.