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Composition operators between area-type Nevanlinna classes. (English) Zbl 1223.47028

This is a translation from [J. Wuhan Univ., Nat. Sci. Ed. 50, No. 1, 1–5 (2004; Zbl 1114.47305)].

Summary: This paper is concerned with composition operators ${C}_{\varphi }$ on area-type Nevanlinna classes ${N}_{a}^{p}$. We give some sufficient and necessary conditions, by constructing the Carleson inequality on ${N}_{a}^{p}$, for the composition operator ${C}_{\varphi }:{N}_{a}^{p}\to {N}_{a}^{q}$ $\left(1 to be bounded or compact. In addition, we also characterize the inducing maps which induce invertible or Fredholm composition operators on ${N}_{a}^{p}$.

##### MSC:
 47B33 Composition operators 30H15 Nevanlinna class and Smirnov class
##### References:
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