$H^2$ - norms of the partial sums of Fourier series by Laguerre basis for bounded holomorphic functions

• Date: 2021
• Main Authors: Savchuk , V. V., Савчук, В. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2021
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2371
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 We compute the upper bounds for $H^2$-norms of the partial sums of Fourier series with respect to the Laguerre basis on the unit ball in the space of bounded holomorphic functions on the unit disk. We give an application of the main result to the solving of some extremal problems of the th...