Fractional SchrÖdinger Equations with Singular Potentials of Higher Order. II: Hypoelliptic Case

Abstract

In this paper we consider the space-fractional Schr\"odinger equation with a singular potential for a wide class of fractional hypoelliptic operators. Such analysis can be conveniently realised in the setting of graded Lie groups. The paper is a continuation and extension of a previous one where the classical Schr\"odinger equation on $\mathbb R^n$ with singular potentials was considered.