Abstract:
The paper puts forward a method for constructing trigonometric Fourier series with L2π-unbounded partial sums that have coefficients with some preassigned properties. In particular, examples of trigonometric Fourier series showing that some conditions of convergence in the mean of trigonometric series cannot be sharpened are constructed.
Citation:
A. S. Belov, “On unimprovability of some theorems on convergence in mean of trigonometric series”, Fundam. Prikl. Mat., 22:1 (2018), 31–49; J. Math. Sci., 250:3 (2020), 404–418
\Bibitem{Bel18}
\by A.~S.~Belov
\paper On unimprovability of some theorems on convergence in mean of trigonometric series
\jour Fundam. Prikl. Mat.
\yr 2018
\vol 22
\issue 1
\pages 31--49
\mathnet{http://mi.mathnet.ru/fpm1780}
\transl
\jour J. Math. Sci.
\yr 2020
\vol 250
\issue 3
\pages 404--418
\crossref{https://doi.org/10.1007/s10958-020-05023-5}
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https://www.mathnet.ru/eng/fpm1780
https://www.mathnet.ru/eng/fpm/v22/i1/p31
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