Abstract
Under certain assumptions on the regularity of a function Φ necessary and sufficient conditions are found for Φ under which the integrability of Φ(¦f¦) implies, for every function f measurable onT 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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Translated from Matematicheskie Zametki, Vol. 52, No. 3, pp. 63–77, September, 1992.
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Konyagin, S.V. Convergence of subsequences of partial cubic sums of Fourier series in mean and almost everywhere. Math Notes 52, 918–930 (1992). https://doi.org/10.1007/BF01209611
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DOI: https://doi.org/10.1007/BF01209611