About Gevrey-\(L^2\)-estimates of pseudo-differential operators associated to the Gevrey symbols (Q2580229)

The first part of the paper is a survey on results of \(L^2\)-boundedness for pseudodifferential operators. In particular, the result of \textit{A. P. Calderón} and \textit{R. Vaillancourt} [Proc. Natl. Acad. Sci. USA 69, 1185--1187 (1972; Zbl 0244.35074)] is recalled. In the second part of the paper the author applies the arguments of Calderón and Vaillancourt to pseudodifferential operators of Gevrey type, and specifies the corresponding estimates for the norm of the operator.