Equivalent definition of some weighted Hardy spaces - Dilnyi, V. M. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
We present the equivalent definition for spaces of functions analytic in the half-plane ${\mathbb C}_+ = \{z: Re z > 0 \}$ for which$$\sup_{|φ| < \frac{π}2} \left\{\int\limits_0^{+∞}\left| f(r e^{iφ})\right|^p e^{-pσ r|\sin φ|} dr \right\} < +∞.$$