Geodesic
General Fourier coefficients and convergence almost everywhere
Izvestiya. Mathematics , Tome 85 (2021) no. 2, pp. 228-240

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We find sufficient conditions which are in a sense best possible that must be satisfied by the functions of an orthonormal system $(\varphi_n)$ in order for the Fourier coefficients of functions of bounded variation to satisfy the hypotheses of the Men'shov–Rademacher theorem. We also prove a theorem saying that every system $(\varphi_n)$ contains a subsystem $(\varphi_{n_k})$ with respect to which the Fourier coefficients of functions of bounded variation satisfy those hypotheses. The results obtained complement and generalize the corresponding results in [1].
Keywords: orthonormal system, functions of bounded variation, Banach space.
Mots-clés : Fourier coefficients 
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     author = {L. D. Gogoladze and G. Cagareishvili},
     title = {General {Fourier} coefficients and convergence almost everywhere},
     journal = {Izvestiya. Mathematics },
     pages = {228--240},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_2_a1/}
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L. D. Gogoladze; G. Cagareishvili. General Fourier coefficients and convergence almost everywhere. Izvestiya. Mathematics , Tome 85 (2021) no. 2, pp. 228-240. http://geodesic.mathdoc.fr/item/IM2_2021_85_2_a1/