Pseudo-differential operators associated with a pair of quadratic-phase Hankel transformations

In this paper, a pair of quadratic-phase Hankel transformations are discussed on certain Zemanian-type spaces. Some estimates of quadratic-phase Hankel (QPH) translation and convolution are obtained. Moreover, two versions of pseudo-differential operators (p.d.o.) associated with quadratic-phase Hankel transformations are defined on some spaces. Furthermore, we have discussed the integral representation of the p.d.o. Using the quadratic-phase Hankel convolution it is shown that p.d.o. satisfy some norm inequalities. Finally, these Hankel-type transformations are utilized to solve some partial differential equations.