Continuity of pseudo-differential operator h μ, a involving Hankel translation and Hankel convolution on some Gevrey spaces

Abstract

The pseudo-differential operator (p.d.o.) h μ, 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 μ, a on Hankel translation τ and Hankel convolution of Gevrey functions is a continuous linear mapping into another Gevrey space.