The product of pseudo-differential operators associated with Bessel operators

The class H-m of symbol 'a' and pseudo-differential operator h(mu,alpha) associated with the Bessel operator S mu = dx(2)/d(2) + 4x(2)/1-4 mu(2) are defined. It is shown that the product of two symbols is a symbol. The product h(mu.a) h(mu,b) Of two pseudo-differential operators h(mu,a) and h(mu,b) associated with symbols a (x, zeta) epsilon H-m and b (y, eta) epsilon H-n is defined. It is proved that h(mu,a) h(mu,b) is a cdntinuous linear mapping of the Zemanian space H-mu into itself. It is shown that the Hankel transform of h(mu),(a) h(mu,b) (u) satisfies a certain L-1-norm inequality.