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