%0 Journal Article
%T Calder¨®n-Zygmund operators related to Laguerre function expansions of convolution type
%A Adam Nowak
%A Tomasz Szarek
%J Mathematics
%D 2011
%I arXiv
%X 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 $\alpha$ in this context. This generalizes a simpler method existing in the literature, but being valid for a restricted range of $\alpha$. 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) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type.
%U http://arxiv.org/abs/1102.1633v1