Annals of Functional Analysis

Bloch--Orlicz functions with Hadamard gaps

Fangwei Chen, Pengcheng Wu, and Congli Yang

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Abstract

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

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

Dates
First available in Project Euclid: 1 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1435764003

Digital Object Identifier
doi:10.15352/afa/06-4-77

Mathematical Reviews number (MathSciNet)
MR3365983

Zentralblatt MATH identifier
1319.47023

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

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

Citation

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. https://projecteuclid.org/euclid.afa/1435764003


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