Wavelet expansions for weighted,vector-valued BMO functions

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 weighted 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 ≠ 2.