Geodesic
About relationship between summability of almost periodic functions and Fouriers coefficients
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 47-54 
Yu. Kh. Khasanov. About relationship between summability of almost periodic functions and Fouriers coefficients. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 47-54. http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a4/
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     title = {About relationship between summability of almost periodic functions and {Fouriers} coefficients},
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     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We generalize Paley's theorem for Bezicovich and Stepanov almost periodic functions on arbitrary trigonometric system. It is proved that for any trigonometric series under some conditions there exists an almost-periodic function which the given series is its Fourier series.

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