Littlewood–Paley–Stein gk-functions for Fourier–Bessel expansions

gk-Functions related to the Poisson semigroup of Fourier–Bessel expansions are defined for each k⩾1. It is proved that these gk-functions are Calderón–Zygmund operators in the sense of the associated space of homogeneous type, hence their mapping properties follow from the general theory.