Continuity of the first Hankel-Clifford transformation on the spaces of the type Hμ are investigated. Pseudo-differential operator h1,μ,a associated with Bessel type operator x Dx2+(1-μ) Dx involving the symbol a (x,y) whose derivatives satisfy certain growth conditions depending on some increasing sequences, is studied on certain ultradifferentiable function spaces. It is shown that the operator h1,μ,a is a continuous linear mapping of one ultradifferentiable function spaces into another spaces of same type. © 2013 Springer Basel.