Bott–Chern harmonic forms on complete Hermitian manifolds

Let (M, J, g, omega) be a Hermitian manifold of complex dimension n. Assume that the torsion of the Chern connection del is bounded, and that there exists a C(infinity)exhausting function rho : M -> R such that del rho, del(2)rho are bounded. We characterize W-1,W-2 Bott-Chern harmonic forms, extending the usual result that holds on compact Hermitian manifolds. Finally, if (M, J, g, omega) is Kahler complete, omega = d eta, with eta bounded, and the sectional curvature is bounded, then we get a vanishing theorem for W-1,W-2 Bott-Chern harmonic (p, q)-forms, if p + q not equal n.