The authors consider the Schrödinger operator
on , , where the nonnegative potential belongs to , which is a class satisfying the following reverse Hölder inequality
for every ball in . The auxiliary function related to is defined as
For , a locally integrable function is said to be in the class if
for all and , where Define . Clearly . For , a locally integrable function is said to be in the class if
for all and .
Denote . For a locally integrable function , the commutators in this paper are defined as
under the assumption that for and . The authors study the boundedness of the commutators and . Especially, they prove that is bounded if and only if Moreover, this conclusion holds true for when .