  In this work, we are interested to develop new directions of the famous
T(1)-theorem. More precisely, we develop a general framework where we look for
replacing the John-Nirenberg space BMO (in the classical result) by a new
BMO_{L}, associated to a semigroup of operators (e^{-tL})_{t>0}. These new
spaces BMO_L (including BMO) have recently appeared in numerous works in order
to extend the theory of Hardy and BMO space to more general situations. Then we
give applications by describing boundedness for a new kind of paraproducts,
built on the considered semigroup. In addition we obtain a version of the
classical T(1) theorem for doubling Riemannian manifolds.
