The pseudodifferential operator \(A(x,D)\) (Q1774669)

Summary: The pseudodifferential operator (p.d.o.) \(A(x,D)\), associated with the Bessel operator \(d^2/dx^2+(1-4\mu^2)/4x^2\), is defined. The symbol class \(H^{m}_{\rho,\delta}\) 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 \(H_\mu\) into itself. An integral representation of the p.d.o.\ is obtained. Using the Hankel convolution, \(L^{p}_{\sigma,\alpha}\)-norm continuity of the p.d.o.\ is proved.