Continuity of pseudo-differential operator h_(μa) involving hankel translation and hankel convolution on some gevrey spaces

摘要

The pseudo-differential operator (p.d.o.) h_(μa) 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_(μa) on Hankel translation t and Hankel convolution of Gevrey functions is a continuous linear mapping into another Gevrey space.