Multipliers and integration operators between conformally invariant spaces.

Abstract

In this paper we are concerned with two classes of conformally invariant spaces of analytic functions in the unit disc D, the Besov spaces Bp (1 <= p < inf) and the Qs spaces (0<s< inf). Our main objective is to characterize for a given pair (X, Y ) of spaces in these classes, the space of pointwise multipliers M(X, Y ), as well as to study the related questions of obtaining characterizations of those g analytic in D such that the Volterra operator Tg or the companion operator Ig with symbol g is a bounded operator from X into Y.