Hankel Type Convolution and Boundedness of Product of Pseudo Differential Type Operators

Abstract

Two symbols are defined in this study utilising the Hankel type transform, as well aspseudo-differential type operators M(x,D) and N(x,D) associated with the Bessel type operator \(\Delta\)\(\alpha\),\(\beta\) defined by equation (2.1) in terms of these symbols.. Further product of M(x,D) and N(x,D) is defined. Sobolev type space is also defined. It is demonstrated that the pseudo-differential type operators M(x,D) , N(x,D) and the product of pseudo-differential type operators are bounded in a certain Sobolev type space associated with the Hankel type transform. Finally, certain unique cases are investigated.