Geodesic
Fourier coefficients of piecewise-monotone functions of several variables
Izvestiya. Mathematics, Tome 62 (1998) no. 2, pp. 247-259 
M. I. Dyachenko. Fourier coefficients of piecewise-monotone functions of several variables. Izvestiya. Mathematics, Tome 62 (1998) no. 2, pp. 247-259. http://geodesic.mathdoc.fr/item/IM2_1998_62_2_a1/
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     author = {M. I. Dyachenko},
     title = {Fourier coefficients of piecewise-monotone functions of several variables},
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     pages = {247--259},
     year = {1998},
     volume = {62},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_2_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

As the main result of this paper we obtain the best possible estimates for the Hardy–Littlewood sums of the Fourier coefficients of piecewise-monotone functions in the spaces $L_p([-\pi,\pi)^m)$, where $2$ .

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