un 2 00 8 BMO functions and Carleson measures with values in uniformly convex spaces

This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let dA and dm denote Lebesgue measures on the unit disc D and the unit circle T, respectively. For 1 < q < ∞ and a Banach space B we prove that there exists a positive constant c such that sup z0∈D Z D (1 − |z|)q−1‖∇f(z)‖qPz0(z) dA(z… (More)