Abstract
We consider Fourier series of summable functions from spaces “wider” than L 1. We describe classes φ(L) which contain conjugate functions, where their conjugate Fourier series converge. The obtained results are more general than A. N. Kolmogorov theorems on the convergence of Fourier series in metrics weaker than that of L 1.
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References
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Original Russian Text © V.I. Filippov, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 7, pp. 21–34.
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Filippov, V.I. On the kolmogorov theorems on Fourier series and conjugate functions. Russ Math. 56, 18–29 (2012). https://doi.org/10.3103/S1066369X12070031
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DOI: https://doi.org/10.3103/S1066369X12070031