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

Keywords: Laguerre bases, Hardy space, partial sum, inner functions

Abstract

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 theory of approximation of holomorphic functions.

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Published
22.01.2021
How to Cite
Savchuk V. V. “$H^2$ - Norms of the Partial Sums of Fourier Series by Laguerre Basis for Bounded Holomorphic Functions”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 1, Jan. 2021, pp. 128 -37, doi:10.37863/umzh.v73i1.2371.
Section
Research articles