The pseudo-differential operator \(h_{\mu,a}\) on some Gevrey spaces (Q1886888)

The authors consider a class of pseudo-differential operators defined via the Hankel transform. Assuming certain Gevrey-type conditions upon the symbols, they prove the continuity of such operators on the generalized Gevrey spaces introduced by \textit{R. S. Pathak} and \textit{K. K. Shrestha} [Integral Transforms Spec. Funct. 11, No. 1, 61--72 (2001; Zbl 0989.46024)]. The Hankel pseudo-differential operators on the Zemanian spaces of smooth functions were investigated by \textit{R. S. Pathak} and \textit{P. K. Pandey} [J. Math. Anal. Appl. 196, No. 2, 736--747 (1995; Zbl 0843.35145)].