LpLp-vanishing results for conformally flat manifolds and submanifolds

In this paper, we first obtain an LpLp-vanishing result for solutions of Simons type equations under spectral assumptions on the relevant Schrödinger operators, and then get some applications to locally conformally flat Riemannian manifolds with constant nonnegative scalar curvature. Furthermore, we get some LpLp-vanishing results for submanifolds.