Pseudo‐differential operators associated with Gyrator transform on Sobolev space

The main aim of this article is to focus on the fundamental properties of the gyrator transform on the Schwartz spaces. A more generalization Hörmander symbol class is introduced and studied the boundedness properties of pseudo‐differential operators associated with the gyrator transform. Integral representation and kernel of the pseudo‐differential operators are derived. It is shown that pseudo‐differential operators satisfies certain norm inequalities on Sobolev space. As an application, we have successfully applied the gyrator transform to solve heat equation and Fredholm integral equation.