  The Pseudo-Differential Operator (p.d.o.) $h_{\mu,a}$ associated with the
Bessel Operator involving the symbol $a(x,y)$ whose derivatives satisfy certain
growth conditions depending on some increasing sequences is studied on certain
Gevrey spaces. The p.d.o. $h_{\mu,a}$ on Hankel translation $\tau$ and Hankel
convolution of Gevrey functions is continuous linear map into another Gevrey
spaces.
