Equivalent definition of some weighted Hardy spaces

• Date: 2008
• Main Authors: Dilnyi, V. M., Дільний, В. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2008
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3241
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We present the equivalent definition for spaces of functions analytic in the half-plane ${\mathbb C}_+ = \{z: Re z > 0 \}$ for which $$\sup_{|\varphi| < \frac{\pi}2} \left\{\int\limits_0^{+\infty}\left| f(r e^{i\varphi})\right|^p e^{-p\sigma r|\sin \varphi|} dr \right\} < +\inft...