The Estimation of Pseudo-differential Operators Utilising the Coupled Fractional Fourier Transform and a Certain Inequality

In this research work, the symbol class Λ (R×R×R×R) is discussed. Then, we give the fundamental properties of this symbol class. Furthermore, the Pseudo-differential operators (p.d.o.) A(x, y,D′x,y) and A(x, y,D′x,y) involving the coupled fractional Fourier transform (CFrFT) Fα1,α2 associated with symbol classes are defined. Finally, inequality and estimate of these operators are also obtained.