Let L = Delta(Hn) + V be a Schrodinger operator on the Heisenberg group H(n), where Delta(Hn) is the sub-Laplacian and the nonnegative potential V belongs to the reverse Holder class B(Q/2). Here Q is the homogeneous dimension H(n). In In this article we investigate the dual space of the Hardy-type space H(L)(I) (H(n)) associated with the Schrodinger operator L. which is a kind of BMO-type space BMO(L) (H(n)) defined by means of a revised sharp function related to the potential V. We give the Fefferman Stein type decomposition of BMO(L)-functions with respect to the (adjoin Riesz transforms (R) over tilde (L)(j) for L, and characterize BMO(L) (H(n)) in terms of the Carleson measure. We also establish the BMO(L)-boundedness of some operators, such as the (adjoin Riesz transforms (R) over tilde (L)(j), the Littlewood-Paley function s(Q)(L), the Lusin area integral S(Q)(L). the Hardy-Littlewood maximal function, and the semigroup maximal function. All results hold for stratified groups as well. (C) 2011 Elsevier Inc. All rights reserved.
