In this paper, using some results of the author on Hankel transform in the Schwartz and Gel’fand-Shilov spaces, we characterize the integral operators of Hankel type which are isomorphisms between the spaces
H
μ
{H_\mu }
of Zemanian. As a particular case, we obtain the classical Zemanian results on Hankel transform, some results of Mendez, and improve some results of Lee. Finally, we use these results to characterize the functions
f
f
of the Schwartz space which satisfy
∫
0
∞
t
α
+
n
f
(
t
)
d
t
=
0
\smallint _0^\infty {t^{\alpha + n}}f(t)dt = 0
for all
n
≥
0
n \geq 0
and
α
>
−
1
\alpha > - 1
.