On the intersection of weighted Hardy spaces
Let $H^p_\sigma( \mathbb{C}_+),$ $1\leq p <+\infty,$ $0\leq \sigma < +\infty,$ be the space of all functions $f$ analytic in the half plane $ \mathbb{C}_{+}= \{ z: \text {Re} z>0 \}$ and such that $$\|f\|:=\sup\limits_{\varphi\in (-\frac{\pi}{2};\frac{\pi}{2})}\left\{\int\limits_0^{+\inf...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vasyl Stefanyk Precarpathian National University
2016-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1428 |
| Summary: | Let $H^p_\sigma( \mathbb{C}_+),$ $1\leq p <+\infty,$ $0\leq \sigma < +\infty,$ be the space of all functions $f$ analytic in the half plane $ \mathbb{C}_{+}= \{ z: \text {Re} z>0 \}$ and such that $$\|f\|:=\sup\limits_{\varphi\in (-\frac{\pi}{2};\frac{\pi}{2})}\left\{\int\limits_0^{+\infty} |f(re^{i\varphi})|^pe^{-p\sigma r|\sin \varphi|}dr\right\}^{1/p}<+\infty.$$ We obtain some properties and description of zeros for functions from the space $\bigcap\limits_{\sigma>0} H^{p}_{\sigma}(\mathbb C_{+}).$ |
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| ISSN: | 2075-9827 2313-0210 |