On the divergence of strong \(\Phi\)-means of Fourier series
type: Item
instance of: scholarly article
title: On the divergence of strong \(\Phi\)-means of Fourier series
zbMATH Open document ID: 0849.42006
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 1995-05-08T00:00:00Z
review text: The author completes the proof of Totik's hypothesis on strong summability of Fourier series. He proves the following theorem: Let \(\Phi\) be a continuous increasing function with \(\Phi(0)= 0\) for which \(\lim_{t\to \infty} (\log \Phi(t))/t= \infty\). Then there exists \(f\in L^1(0, 2\pi)\) such that \[ \lim_{n\to \infty} {1\over n} \sum^n_{k= 1} \Phi(|S_k(x, f)|)= \infty\quad \text{a.e.}, \] where \(S_k(x, f)\) is the partial sum of the Fourier series of \(f\).
Mathematics Subject Classification ID: 42A24
zbMATH DE Number: 751097
zbMATH Keywords: strong summability of Fourier series
author: G. Karagulyan
reviewed by: W. Łenski
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 751097