Commutators of Riesz transforms of magnetic Schrodinger operators

Let A = -(del - i (a) over right arrow) . (del - i (a) over right arrow) + V be a magnetic Schrodinger operator acting on L-2(R-n), n >= 1, where (a) over right arrow = (a(1), ... , a(n)) epsilon L-loc(2)(R-n, R-n) and 0 <= V epsilon L-loc(1)(R-n). In this paper, we show that when a function b epsilon BMO(R-n), the commutators [b, T-k] f = T-k(bf) - bT(k) f, k = 1, ... , n, are bounded on L-p(R-n) for all 1 < p < 2, where the operators T-k are Riesz transforms (partial derivative/partial derivative x(k) - ia(k))A(-1/2) associated with A.