A Calderón–Zygmund operator of higher order Schrödinger type

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 show that an operator of higher order Schrödinger type is a Calderón-Zygmund operator. We also show that there exist potentials which satisfy our assumptions but are not nonnegative polynomials. C 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim for all V satisfying V ≥ 0 and V ∈ L 1 loc (R n ) ([12, page 419]).