Hilbert Transforms Associated with Dunkl-Hermite Polynomials

Details Hilbert Transforms Associated with Dunkl-Hermite Polynomials Hilbert Transforms Associated with Dunkl-Hermite Polynomials

2009-03-25

arxiv.org/abs/0903.4369v1

SIGMA 5 (2009), 037, 17 pages

Mathematics

Classical Analysis and ODEs

Scientific paper

10.3842/SIGMA.2009.037

We consider expansions of functions in $L^{p}(\mathbb{R},|x|^{2k}dx)$, $1\leq p<+\infty$ 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.

Affiliated with

Also associated with

No associations

Rating

Hilbert Transforms Associated with Dunkl-Hermite Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hilbert Transforms Associated with Dunkl-Hermite Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hilbert Transforms Associated with Dunkl-Hermite Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-68548