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

Details Calderón-Zygmund operators related to Laguerre function expansions of convolution type Calderón-Zygmund operators related to Laguerre function expansions of convolution type

2011-02-08

arxiv.org/abs/1102.1633v1

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

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.

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