Some properties of the pseudo-differential operator hμ,a

The kernel K(x,y) of the pseudo-differential operator hμ,a is defined. It is shown that the kernel is a continuous function. It is proved that the pseudo-differential operator hμ,a is pseudolocal. A global regularity result for an elliptic partial differential operator is obtained. An existence theorem for the weak solution of a pseudo-differential equation is established.