On the uniform convergence of negative order Cesaro means of Fourier series

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• 作者：M.G. Grigoryan ; ^{gmarting@ysu.am" class="auth_mail" title="E-mail the corresponding author} ; L.N. Galoyan ^{levongaloyan@ysu.am" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Cesaro means ; Uniform convergence ; Density ; Rudin&ndash ; Shapiro sequence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：434
• 期：1
• 页码：554-567
• 全文大小：343 K

文摘

The paper investigates the uniform convergence of negative order Cesaro means of Fourier series of continuous functions after correction of these functions on a set of small measure. We also give an example of continuous function, the (C,α)$(C,\alpha )$ means of Fourier series of which diverge over any subsequence on the set of positive measure for any $\alpha \in (-1,-\frac{1}{2})$.