On the intersection of weighted Hardy spaces
Journal Title: Карпатські математичні публікації - Year 2016, Vol 8, Issue 2
Abstract
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 $\bigcap\limits_{\sigma>0} H^{p}_{\sigma}(\mathbb C_{+})$.
Authors and Affiliations
V. Dilnyi, T. Hishchak
Keywords
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- EP ID EP326990
- DOI 10.15330/cmp.8.2.224-229
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