On the intersection of weighted Hardy spaces - Dilnyi, V.M.; Hishchak, T.I. (Carpathian Mathematical Publications, 2016)
Let $H^p_σ( \mathbb{C}_+),$ $1≤ p <+∞,$ $0≤ σ < +∞,$ be the space of all functions $f$ analytic in the half plane $ \mathbb{C}_{+}= \{ z: \text {Re} z>0 \}$ and such that $$\|f\|:=\sup\limits_{φ\in (-\frac{π}{2};\frac{π}{2})}\left\{\int\limits_0^{+∞} |f(re^{iφ})|^pe^{-pσ r|\sin φ|}dr\right\}^{1/p}<+∞.$$ We obtain some properties and description of zeros for functions from the space $\bigcap\limits_{σ>0} H^{p}_{σ}(\mathbb C_{+}).$