  We introduce a scale of weighted Carleson norms, which depend on an
integrability parameter p, where p=2 corresponds to the classical Carleson
measure condition. Relations between the weighed BMO norm of a vector-valued
function f:R->X, and the Carleson norm of the sequence of its wavelet
coefficients, are established. These extend the results of
Harboure-Salinas-Viviani, also in the scalar-valued case when p is not 2.

Functional Analysis