Calderón–Zygmund operators related to Laguerre function expansions of convolution type

Abstract

We develop a technique of proving standard estimates in the setting of Laguerre function expansions of convolution type, which works for all admissible type multi-indices α in this context. This generalizes a simpler method existing in the literature, but being valid for a restricted range of α. As an application, we prove that several fundamental operators in harmonic analysis of the Laguerre expansions, including maximal operators related to the heat and Poisson semigroups, Riesz transforms, Littlewood–Paley–Stein type square functions and multipliers of Laplace and Laplace–Stieltjes transforms type, are (vector-valued) Calderón–Zygmund operators in the sense of the associated space of homogeneous type.