Continuity of Pseudo-Differential Operator $h_{\hat{I}¼,a}$ Involving Hankel Translation and Hankel Convolution on Some Gevrey Spaces

Abstract

The Pseudo-Differential Operator (p.d.o.) $h_{\hat{I}¼,a}$ associated with the Bessel Operator involving the symbol $a(x,y)$ whose derivatives satisfy certain growth conditions depending on some increasing sequences is studied on certain Gevrey spaces. The p.d.o. $h_{\hat{I}¼,a}$ on Hankel translation $\ddot{I}„$ and Hankel convolution of Gevrey functions is continuous linear map into another Gevrey spaces.