  Let L be a Schr\"odinger operator of the form L=-\Delta+V acting on
L^2(\mathbb R^n) where the nonnegative potential V belongs to the reverse
H\"older class B_q for some q>= n. Let BMO denote the BMO space associated to
the Schr\"odinger operator L. In this article we will show that a function f in
BMO_L is the trace of the solution of u_t+L u=0, u(x,0)= f(x), where u
satisfies a Carleson-type condition. Conversely, this Carleson condition
characterizes all the L-carolic functions whose traces belong to the space
BMO_L. This result extends the analogous characterization founded by Fabes and
Neri for the classical BMO space of John and Nirenberg.
