The commutator of the Kato square root for second order elliptic operators on .n

Let L = .div(A.) be a second order divergence form elliptic operator, and A be an accretive, n.n matrix with bounded measurable complex coefficients in .n. We obtain the L p bounds for the commutator generated by the Kato square root L... and a Lipschitz function, which recovers a previous result of Calderón, by a different method. In this work, we develop a new theory for the commutators associated to elliptic operators with Lipschitz function. The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory.