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.