The multiplier of the interval [−1, 1] for the Dunkl transform on the real line

We study the boundedness of the multiplier of the interval [−1, 1] for the Dunkl transform of order α −1/2 on weighted Lp spaces, with 1 < p < ∞. In particular, we get that it is bounded from Lp(R, |x|2α+1 dx) into itself if and only if 4(α +1)/(2α + 3) < p<4(α +1)/(2α + 1). © 2006 Elsevier Inc. All rights reserved