Annals of Functional Analysis

Bloch--Orlicz functions with Hadamard gaps

Fangwei Chen, Pengcheng Wu, and Congli Yang

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In this paper, we give a sufficient and necessary condition for an analytic function $f(z)$ on the unit disc $\mathbb{D}$ with Hadamard gaps, that is, $f(z)=\sum\limits_{k=1}^{\infty}a_kz^{n_k}$, where $\frac{n_{k+1}}{n_k}\geq\lambda>1$ for all $k\in \mathbb{N}$, belongs to the Bloch--Orlicz space $ \mathcal{B}^{\varphi}$. As an application of our results, the compactness of composition operator are discussed.

Article information

Ann. Funct. Anal., Volume 6, Number 4 (2015), 77-89.

First available in Project Euclid: 1 July 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B33: Composition operators
Secondary: 30H99: None of the above, but in this section

Bloch--Orlicz space $\mathcal{Q}_{k}$ type space Hadamard gap composition operator


Yang, Congli; Wu, Pengcheng; Chen, Fangwei. Bloch--Orlicz functions with Hadamard gaps. Ann. Funct. Anal. 6 (2015), no. 4, 77--89. doi:10.15352/afa/06-4-77.

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