On One Uniqueness Theorem for a Weighted Hardy Space

A uniqueness theorem is proved for the space of functions analytic in the right half plane and satisfying the condition supφ<π2∫0+∞freiφpe−pσrsinφdr<+∞.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \underset{\left|\upvarphi \right|<\frac{\uppi}{2}}{ \sup}\left\{{\displaystyle \underset{0}{\overset{+\infty }{\int }}{\left|f\left(r{e}^{i\varphi}\right)\right|}^p{e}^{-p\sigma r\left| \sin \varphi \right|}dr}\right\}<+\infty . $$\end{document}