Boundedness of Operators on Campanato Spaces Related with Schrodinger Operators on Heisenberg Groups

Let L = -Delta(Hn) + V be a Schrodinger operator on Heisenberg groups H-n, where Delta(Hn) is the sub-Laplacian and the nonnegative potential V belongs to the reverse Holder class B-q, q >= Q/2 and Q = 2n +2 is the homogeneous dimension of . We establish a T1 criterion for the boundedness of gamma-Schrodinger-Calderon-Zygmund operators on Campanato type spaces BMOL alpha(H-n). As an application, by the aid of regularity estimate for fractional heat semigroup (e(-tL beta)}(t>0), we prove the BMOL alpha-boundedness of operators generated by fractional heat semigroups including the maximal operators, the square functions, the Laplace transform type multipliers and the fractional integral associated with SchrOdinger operator L via T1 theorem, respectively.