Abstract
In this paper, we give an L
p
−L
q
-version of Morgan's theorem for the Dunkl-Bessel transform ℱ
D, B
on
. More precisely, we prove that for all 1≤p, q≤+∞, α>2, η=α/(α−1) and a>0, b>0, then for all measurable function f on
, the conditions
and
imply f=0, if and only if (aα)
1/α
(b η)
1/η
>(sin(π/2)(η−1))
1/η
, where
, are the Lebesgue spaces associated with the Dunkl-Bessel transform.