L^p Estimates of Higher Order Parabolic Schrödinger Type Operators

Abstract

In this paper, we consider the higher order parabolic Schrödinger type operator with nonnegative potentials. We assume that the nonnegative potential belongs to both the reverse Hölder class and the Gaussian class. Using the pointwise estimates of Hardy-Littlewood maximal operator, we establish L^p boundedness of Riesz transforms associated with the higher order parabolic Schrödinger type operator.