Let Lk =(-△)k + V k be a Schrdinger type operator,where k ≥ 1 is a positive integer and V is a nonnegative polynomial.We obtain the Lp estimates for the operators ▽2k Lk-1 and ▽k Lk-1/2.
Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.
