Morrey spaces in quantum theory: on regularity of the solution of Schrödinger equation via fractional maximal operators

Abstract

In this paper, we investigate the regularity conditions of solutions of Schrödinger Equations with forcing function in the framework of generalized weighted Morrey spaces. We utilize the established boundedness of the fractional maximal operator on generalized weighted Morrey spaces. We prove that if the forcing function does not balance local regularity and global decay, then the solution of the equation does not do so either.