This article is cited in 2 papers

On the Kolmogorov theorems on Fourier series and conjugate functions

V. I. Filippov

Chair of Applied Mathematics and Information Science, Saratov State Social-Economic University, Saratov, Russia

Abstract: We consider Fourier series of summable functions from spaces wider than $L_1$. We describe classes $\varphi(L)$ which contain conjugate functions, where their conjugate Fourier series converge. The obtained results are more general than the A. N. Kolmogorov theorems on the convergence of Fourier series in metrics weaker than $L_1$.

Keywords: Fourier series, conjugate functions, generalized Orlicz spaces, classes $\varphi(L)$.

UDC: 517.51+517.52

Received: 25.07.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:7, 18–29

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