Abstract
We consider expansions of functions in L p (R,|x| 2k dx), 1 p < +1 with respect to Dunkl-Hermite functions in the rank-one setting. We actually define the heat-diffusion and Poisson integrals in the one-dimensional Dunkl setting and study their properties. Next, we define and deal with Hilbert transforms and conjugate Poisson integrals in the same setting. The formers occur to be Calderon-Zygmund operators and hence their mapping properties follow from general results.
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