Some Estimates for Riesz Transforms Associated with Schrodinger Operators

L = -delta + V be the Schrodinger operator on R-n, where n >= 3, and nonnegative potential V belongs to the reverse Holder class RH(q )with n/2 < q < n. Let H-L(p),(R-n) denote the Hardy space related to L and BMOL(R-n) denote the dual space of H-L(1)(R-n). In this paper, we show that T-alpha,T-beta = (VVL)-V-alpha-beta is bounded from H(L)(p)1 , (R-n) for n/n+delta into L-p2(R-n) for n/n + delta' < p(1) < 1 and 1/p2 1 = 1/P1- 2(beta - alpha)/n , where delta' = min{1, 2 - n/q(0)} and q(0) is the reverse Holder index of V. Moreover, we prove T-alpha,T-beta* is bounded on BMOL(R-n) when beta - alpha = 1/2