  Let L be a generator of a semigroup satisfying the Gaussian upper bounds. In
this paper, we study further a new BMO_L space associated with L which was
introduced recently by Duong and Yan. We discuss applications of the new BMO_L
spaces in the theory of singular integration such as BMO_L estimates and
interpolation results for fractional powers, purely imaginary powers and
spectral multipliers of self adjoint operators. We also demonstrate that the
space BMO_L might coincide with or might be essentially different from the
classical BMO space.
