L^p Boundedness of Higher Order Schrödinger Type Operators

Abstract

We consider higher order Schrödinger type operators with nonnegative potentials. We assume that the potential belongs to the reverse Hölder class which includes nonnegative polynomials. We establish estimates of the fundamental solution and show L^p boundedness of some Schrödinger type operators. We use pointwise estimates by the Hardy-Littlewood maximal operator to prove our results.