Tauberian theorems for Nörlund summability and their application to the convergence of Fourier series (Q268049)

The author obtains Tauberian theorems for Nörlund summability methods in Section 3. His results generalize well-known Tauberian theorems. In Section 4, the author presents a corrected proof of a one-sided Tauberian theorem for Nörlund summability which was stated by \textit{K. S. K. Iyengar} [Proc. Indian Acad. Sci., Sect. A 18, 113--120 (1943; Zbl 0060.18501)] and defectively proved by \textit{O. P. Varshney} [Tohoku Math. J. (2) 16, 105--110 (1964; Zbl 0133.01302)] and establishes corresponding \(O\)-Tauberian theorems. In Section 5, the author studies the relationship between the Tauberian theorems given in Sections 3 and 4. In Section 6, the author applies his results to the convergence of Fourier series.