## Annals of Functional Analysis

### Hadamard gap series in weighted-type spaces on the unit ball

#### Abstract

We give a sufficient and necessary condition for an analytic function $f(z)$ on the unit ball $\mathbb{B}$ in $\mathbb{C}^{n}$ with Hadamard gaps, that is, for $f(z)=\sum_{k=1}^{\infty}P_{n_{k}}(z)$ where $P_{n_{k}}(z)$ is a homogeneous polynomial of degree $n_{k}$ and $n_{k+1}/n_{k}\ge c\gt 1$ for all $k\in\mathbb{N}$, to belong to the weighted-type space $H^{\infty}_{\mu}$ and the corresponding little weighted-type space $H^{\infty}_{\mu,0}$ under some condition posed on the weighted funtion $\mu$. We also study the growth rate of those functions in $H^{\infty}_{\mu}$.

#### Article information

Source
Ann. Funct. Anal., Volume 8, Number 2 (2017), 259-269.

Dates
Accepted: 16 September 2016
First available in Project Euclid: 1 March 2017

https://projecteuclid.org/euclid.afa/1488358821

Digital Object Identifier
doi:10.1215/20088752-0000011X

Mathematical Reviews number (MathSciNet)
MR3619321

Zentralblatt MATH identifier
1361.32007

#### Citation

Hu, Bingyang; Li, Songxiao. Hadamard gap series in weighted-type spaces on the unit ball. Ann. Funct. Anal. 8 (2017), no. 2, 259--269. doi:10.1215/20088752-0000011X. https://projecteuclid.org/euclid.afa/1488358821

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