On the Hausdorff summability of series associated with a Fourier and its allied series
Annales de l'Institut Fourier, Volume 21 (1971) no. 3, p. 173-179

Recently, Tripathy - Jour. Ind. Math. Soc., 32 (1960), 141-154 - has proved some results on absolute Hausdorff summability of some series associated with Fourier series and its allied series, which generalise the results proved by Mohanty on absolute Cesaro summability. Proceeding on the similar lines, the author has generalised the results of Cheng - Duke Math. Jour., 15 (1948), 17-27 - by proving them on absolute Hausdorff summability.

Récemment, Tripathy - Jour. Ind. Math. Soc., 32 (1960), 141-154 - a démontré certains résultats sur la sommabilité absolue de Hausdorff de séries associées à des séries de Fourier et des séries qui s’y rattachent, résultats qui généralisent ceux démontrés par Mohanty sur la sommabilité absolue de Cesaro.

En procédant de façon analogue, l’auteur a généralisé les résultats de Cheng - Duke Math. Jour., 15 (1948), 17-27 - en les démontrant pour la sommabilité absolue de Hausdorff.

@article{AIF_1971__21_3_173_0,
author = {Gupta, B. L.},
title = {On the Hausdorff summability of series associated with a Fourier and its allied series},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Louis-Jean},
volume = {21},
number = {3},
year = {1971},
pages = {173-179},
doi = {10.5802/aif.384},
zbl = {0222.42006},
mrnumber = {49 \#3426},
language = {en},
url = {http://www.numdam.org/item/AIF_1971__21_3_173_0}
}

Gupta, B. L. On the Hausdorff summability of series associated with a Fourier and its allied series. Annales de l'Institut Fourier, Volume 21 (1971) no. 3, pp. 173-179. doi : 10.5802/aif.384. http://www.numdam.org/item/AIF_1971__21_3_173_0/

[1] M.T. Cheng, Summability factors of Fourier series, Duke Math. Jour : 15 (1948), 17-27. | MR 9,580d | Zbl 0030.24901

[2] G.H. Hardy, Divergent series. Oxford 1949. | MR 11,25a | Zbl 0032.05801

[3] B. Kuttner, On the “second theorem of consistency” for riesz summability (II), Jour. Lond. Math. Soc. 27 (1952), 207-217. | MR 13,738a | Zbl 0046.06302

[4] N. Tripathy, On the absolute Hausdorff summability of some series associated with Fourier series and its allied series, Jour. Ind., Math. Soc. 32 (1960) 141-154. | MR 41 #725 | Zbl 0192.42401