A strengthened form of a theorem of Fejér
Compositio Mathematica, Volume 21 (1969) no. 3, p. 262-270 
@article{CM_1969__21_3_262_0,
     author = {Siddiqi, Jamil A.},
     title = {A strengthened form of a theorem of Fej\'er},
     journal = {Compositio Mathematica},
     publisher = {Wolters-Noordhoff Publishing},
     volume = {21},
     number = {3},
     year = {1969},
     pages = {262-270},
     zbl = {0177.31802},
     mrnumber = {256062},
     language = {en},
     url = {http://www.numdam.org/item/CM_1969__21_3_262_0}
}

Siddiqi, Jamil A. A strengthened form of a theorem of Fejér. Compositio Mathematica, Volume 21 (1969) no. 3, pp. 262-270. http://www.numdam.org/item/CM_1969__21_3_262_0/

L. Fejér [1 ] Ûber die Bestimmung des Sprunges einer Funktionen aus ihrer Fourierreihe, J. Reine Angew. Math, 142 (1913), 165-168. | JFM 44.0483.01

J.A. Siddiqi [2] Coefficient properties of certain Fourier series, Math. Ann., 181 (1969), 242-254. | MR 243260 | Zbl 0164.07302

N. Wiener [3] The quadratic variation of a function and its Fourier coefficients, J. Math. and Phys. 3 (1924), 72-94. | JFM 50.0203.01

A. Zygmund [4] Trigonometric Series vol. 1, Cambridge, 1959. | Zbl 0085.05601