  In this paper we establish a T1 criterion for the boundedness of
Hermite-Calderon-Zygmund operators on the BMO_H(R^n) space naturally associated
to the Hermite operator H. We apply this criterion in a systematic way to prove
the boundedness on BMO_H(R^n) of certain harmonic analysis operators related to
H (Riesz transforms, maximal operators, Littlewood-Paley g-functions and
variation operators).
