The pseudodifferential operator (p.d.o.) A ( x , D ) , associated with the Bessel operator d 2 / d x 2 + ( 1 − 4 μ 2 ) / 4 x 2 , is defined. Symbol class H ρ , δ m is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space H μ into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution L σ , α p -norm continuity of the p.d.o. is proved.