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 $${\mathbb D}$$ , the Besov spaces $$B^p (1\le p<\infty )$$ and the $$Q_s$$ spaces $$(0<s<\infty )$$ . 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 $${\mathbb D}$$ such that the Volterra operator $$T_g$$ or the companion operator $$I_g$$ with symbol g is a bounded operator from X into Y.