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Mat. Zametki, 1992, Volume 52, Issue 3, Pages 63–77 (Mi mz4701)  

Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere

S. V. Konyagin

M. V. Lomonosov Moscow State University

Abstract: Under certain assumptions on the regularity of a function $\Phi$ necessary and sufficient conditions are found for $\Phi$ under which the integrability of $\Phi(|f|)$ implies, for every function $f$ measurable on $T^d$, the existence of a subsequence of cubic sums of the Fourier series of $f$ that converges to f in mean or almost everywhere.

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English version:
Mathematical Notes, 1992, 52:3, 918–930

Bibliographic databases:

Document Type: Article
UDC: 517.51
Received: 26.03.1992

Citation: S. V. Konyagin, “Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere”, Mat. Zametki, 52:3 (1992), 63–77; Math. Notes, 52:3 (1992), 918–930

Citation in format AMSBIB
\Bibitem{Kon92}
\by S.~V.~Konyagin
\paper Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere
\jour Mat. Zametki
\yr 1992
\vol 52
\issue 3
\pages 63--77
\mathnet{http://mi.mathnet.ru/mz4701}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1194129}
\zmath{https://zbmath.org/?q=an:0789.42007}
\transl
\jour Math. Notes
\yr 1992
\vol 52
\issue 3
\pages 918--930
\crossref{https://doi.org/10.1007/BF01209611}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992LF91500007}


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