Some mathematical properties of two versions of pseudo-differential operators involving the coupled fractional Fourier transform

Abstract

The Pseudo-differential operators (p.d.o.) A(x,y,Dx′,y) and A(x,y,Dx′,y) involving the coupled fractional Fourier transform Fα1,α2 are defined. The symbol class Λ(R× R× R× R)) is discussed. We conclude the manuscript by applying some of the results to obtain some inequalities. At the end, boundedness of the Pseudo-differential operators are also discussed.