Commutators with fractional differentiation for second-order elliptic operators on ℝn

Let L = −div(A∇) be a second-order divergence form elliptic operator and A an accretive, n × n matrix with bounded measurable complex coefficients in ℝn. In this paper, we establish Lp theory for the commutators generated by the fractional differential operators related to L and bounded mean oscillation (BMO)–Sobolev functions.