An L p version of Hardy's theorem for the Jacobi-Dunkl transform

• Published in: Integral transforms and special functions Vol. 15; no. 3; pp. 225 - 237
• Main Authors: Chouchane, F., Mili†, M., Trimèche‡, K.
• Format: Journal Article
• Language: English
• Published: Taylor & Francis Group 01.06.2004
• Subjects: Hardy's theorem; Jacobi-Dunkl transform
• ISSN: 1065-2469; 1476-8291
• DOI: 10.1080/10652460310001600690

In this paper, we give a generalization of Hardy's theorem for the Jacobi-Dunkl transform ℱ on ℝ. More precisely for all a > 0, b > 0 and p, q ∈ [1, +∞], we determine the measurable functions f on ℝ such that E 1/4a −1 f ∈ L α,β p (ℝ) and e bλ 2 ℱf ∈ L σ q (ℝ), where E t , t > 0, L α,β p (ℝ), p ∈ [1, +∞], and L σ q (ℝ), q ∈ [1, +∞], are respectively the heat kernel and the Lebesgue spaces associated with the Jacobi-Dunkl operator. * E-mail: fredj.chouchane@ipeim.rnu.tn † E-mail: maher.mili@fsm.rnu.tn ‡ E-mail: mohamed.sifi@fst.rnu.tn