On strong Nörlund summability of Fourier series

Abstract

In this note, a sufficient condition for summability [ N , p n ( 1 ) , 2 ] of Fourier series has been obtained which in conjunction with the author's Tauberian theorem [M.L. Mittal, A Tauberian theorem on strong Nörlund summability, J. Indian Math. Soc. 44 (1980) 369–377] on strong Nörlund summability gives a sufficient condition for summability [ C , 1 , 2 ] of a Fourier series. This generalizes results due to Prasad [G. Prasad, On strong Nörlund summability of Fourier series, Univ. Roorkee Res. J. 9 (1966–1967) 1–10] and Varshney [O.P. Varshney, Note on H 2 summability of Fourier series, Boll. Un. Mat. Ital. 16 (1961) 383–385].