In this work, we investigate a class of degenerate Schrödinger equations associated to degenerate elliptic operators with irregular potentials on Formula: see text by introducing a suitable Hörmander metric Formula: see text and a Formula: see text-weight Formula: see text. We establish the well-posedness for the corresponding degenerate Schrödinger and degenerate parabolic equations. When the subellipticity is available on the degenerate elliptic operator we deduce spectral properties for a class of degenerate Hamiltonians. We also investigate the Formula: see text mapping properties for operators with symbols in the Formula: see text classes in the spirit of classical Fefferman’s Formula: see text-bounds for the Formula: see text calculus. Finally, within our Formula: see text-classes, sharp Formula: see text-estimates and Schatten–von Neumann properties for Schrödinger operators for Hörmander sums of squares are also investigated.
Cardona et al. (Tue,) studied this question.