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Zbl 1223.47028
Wang, Mao-Fa; Liu, Pei-De
Composition operators between area-type Nevanlinna classes. (English)
[J] Front. Math. China 1, No. 2, 293-302 (2006); translation from J. Wuhan Univ. Natur. Sci. Ed. 50, No. 1, 1-5 (2004). ISSN 1673-3452; ISSN 1673-3576/e

This is a translation from [J. Wuhan Univ., Nat. Sci. Ed. 50, No. 1, 1--5 (2004; Zbl 1114.47305)]. \par 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 $N^p_a$, for the composition operator $C_\varphi:N^p_a \to N^q_a$ $(1<p\le q)$ to be bounded or compact. In addition, we also characterize the inducing maps which induce invertible or Fredholm composition operators on $N^p_a$.

MSC 2000:: *47B33 Composition operators
30H15

Keywords: composition operator; Fredholm operator; Nevanlinna class; Carleson measure

Citations: Zbl 1114.47305

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