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.
Citation
Fangwei Chen. Pengcheng Wu. Congli Yang. "Bloch--Orlicz functions with Hadamard gaps." Ann. Funct. Anal. 6 (4) 77 - 89, 2015. https://doi.org/10.15352/afa/06-4-77
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