# Multipliers and integration operators between conformally invariant spaces

## TL;DR

This paper characterizes pointwise multipliers and bounded Volterra and companion operators between conformally invariant spaces of analytic functions, specifically Besov and Q_s spaces, in the unit disk.

## Contribution

It provides new characterizations of multipliers and operator boundedness between Besov and Q_s spaces, advancing understanding of conformally invariant function spaces.

## Key findings

- Characterization of pointwise multipliers between Besov and Q_s spaces
- Conditions for boundedness of Volterra operators between these spaces
- Conditions for boundedness of companion operators between these 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 $B^p$ $(1\le p<\infty )$ 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 $\D $ such that the Volterra operator $T_g$ or the companion operator $I_g$ with symbol $g$ is a bounded operator from $X$ into $Y$.