On integral representations in the Hardi classes and on the best approximations in some functional spaces

• Date: 1991
• Main Authors: Dovgoshei , A. A., Довгошей , А. А.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1991
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/9613
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For the case of a simply connected domain in the plane one proves necessary and sufficient conditions for the representation of functions of the Hardy class $H^1$ by an integral with respect to the harmonic measure of its boundary values. A theorem is given, characterizing the rate of decrease of th...