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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 7, Pages 21–34 (Mi ivm8717)  
This article is cited in 2 scientific papers (total in 2 papers)

On the Kolmogorov theorems on Fourier series and conjugate functions

V. I. Filippov

Chair of Applied Mathematics and Information Science, Saratov State Social-Economic University, Saratov, Russia
Full-text PDF (235 kB) Citations (2)
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Abstract: We consider Fourier series of summable functions from spaces wider than $L_1$. We describe classes $\varphi(L)$ which contain conjugate functions, where their conjugate Fourier series converge. The obtained results are more general than the A. N. Kolmogorov theorems on the convergence of Fourier series in metrics weaker than $L_1$.
Keywords: Fourier series, conjugate functions, generalized Orlicz spaces, classes $\varphi(L)$.
Received: 25.07.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 7, Pages 18–29
DOI: https://doi.org/10.3103/S1066369X12070031
Bibliographic databases:
Document Type: Article
UDC: 517.51+517.52
Language: Russian
Citation: V. I. Filippov, “On the Kolmogorov theorems on Fourier series and conjugate functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 7, 21–34; Russian Math. (Iz. VUZ), 56:7 (2012), 18–29
Citation in format AMSBIB
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\by V.~I.~Filippov
\paper On the Kolmogorov theorems on Fourier series and conjugate functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 7
\pages 21--34
\mathnet{http://mi.mathnet.ru/ivm8717}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3077459}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 7
\pages 18--29
\crossref{https://doi.org/10.3103/S1066369X12070031}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866290722}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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