Hilbert Transforms Associated with Dunkl-Hermite Polynomials
Classical Analysis and ODEs
2009-03-26 v1
Abstract
We consider expansions of functions in , 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 Calder\'on-Zygmund operators and hence their mapping properties follow from general results.
Cite
@article{arxiv.0903.4369,
title = {Hilbert Transforms Associated with Dunkl-Hermite Polynomials},
author = {Néjib Ben Salem and Taha Samaali},
journal= {arXiv preprint arXiv:0903.4369},
year = {2009}
}