**Songxiao Li**

## Composition Operators on $Q_p$ Spaces

**Abstract:**

Suppose that $\phi$ is a nonconstant analytic self-mapping of the unit disk~$D$.
Necessary or sufficient conditions for the composition operator $C_\phi:Q_q \rightarrow
Q_{p}$ to be bounded or compact are given in terms of $\phi$. The
function-theoretic characterization of the compactness of the composition
operator $C_\phi:Q_q \rightarrow Q_{p,0}$ is also given.

**Keywords:**

Composition operator, space $Q_p$, space $Q_{p,0}$.

**MSC 2000:** Primary: 47B35. Secondary: 30H05