Besov Spaces, Multipliers and Univalent Functions

We let B (p) (1 a parts per thousand currency sign p < a) denote the conformally invariant Besov spaces of analytic functions in the unit disc . Our main objective in this article is to investigate the basic problem of the boundedness of multiplication operators between Besov spaces looking for checkable descriptions of the spaces of multipliers M(B (p) , B (q) ), 1 a parts per thousand currency sign p, q < a, and giving an extense class of explicit examples of such multipliers. We study also some basic types of functions in M(B (p) , B (q) ) spaces; loosely speaking, we investigate which functions of certain important types (lacunary series, univalent functions, "modified"-inner functions) are to be found in the spaces M(B (p) , B (q) ).