VECTOR-VALUED ANALYTIC FUNCTIONS OF BOUNDED MEAN OSCILLATION AND GEOMETRY OF BANACH SPACES

摘要

When dealing with vector-valued functions, sometimes is rather difficult to give non trivial examples, meaning examples which do not come from tensoring scalar-valued functions and vectors in the Banach space, belonging to certain classes. This is the situation for vector valued BMO. One of the objectives of this paper is to look for methods to produce such examples. Our main tool will be the vector-valued extension of the following result on multipliers, proved in [MP], which says that the space of multipliers between H~1 and BMOA can be identified with the space of Bloch functions B, i.e. (H~1, BMOA) = B (see Section 3 for notation), which, in particular gives g * f ∈ BMOA whenever f ∈ H~1 and g ∈ B.