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