Multipliers and integration operators between conformally invariant spaces

In this paper we are concerned with two classes of conformally invariant spaces of analytic functions in the unit disc $\text{D}$, the Besov spaces $B^p$ $(1\le p<\mathrm{\infty })$ and the $Q_s$ spaces $(0<s<\mathrm{\infty })$. 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 $\text{D}$ such that the Volterra operator $T_g$ or the companion operator $I_g$ with symbol $g$ is a bounded operator from $X$ into $Y$.