Boundedness of High Order Commutators of Riesz Transforms Associated with Schr?dinger Type Operators

Let L;=（-?）;+ V;be the Schr?dinger type operator, where V■0 is a nonnegative potential and belongs to the reverse H?lder class RH;for q;> n/2, n ≥5. The higher Riesz transform associated with L;is denoted by ■and its dual is denoted by ■. In this paper, we consider the m-order commutators [b;, R] and [b;, R*], and establish the（L;, L;）-boundedness of these commutators when b belongs to the new Campanato space Λ;（ρ） and 1/q = 1/p-mβ/n.