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Izvestiya: Mathematics, 2009, Volume 73, Issue 2, Pages 301–318
DOI: https://doi.org/10.1070/IM2009v073n02ABEH002447 (Mi im1131) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Fourier series of functions with a non-summable derivative

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky, Faculty of Mathematics and Mechanics
English version PDF (274 kB) Citations (1)
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DOI: https://doi.org/10.1070/IM2009v073n02ABEH002447
Abstract: We consider the convergence of Fourier series in the norm of Orlicz spaces narrower than $L(e^x)$. It is shown that if a continuous function has a non-summable derivative, then its Fourier series is not necessarily convergent in the norm of these Orlicz spaces. We find a condition on a bounded function $f$ under which the Fourier series of $f$ is convergent in the norm of an Orlicz space $L(\varphi)\subset L(e^x)$ and estimate the accuracy of this result.
Keywords: Fourier series, convergence, Lorentz spaces, local modulus of continuity.
Received: 10.07.2006
Revised: 26.06.2007
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2009, Volume 73, Issue 2, Pages 91–108
DOI: https://doi.org/10.4213/im1131
Bibliographic databases:
UDC: 517.51
MSC: 41A25, 41A55, 65L10, 65R20, 42A15, 65T40, 65J105, 46A45, 46BXX
Language: English
Original paper language: Russian
Citation: S. F. Lukomskii, “Fourier series of functions with a non-summable derivative”, Izv. RAN. Ser. Mat., 73:2 (2009), 91–108; Izv. Math., 73:2 (2009), 301–318
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v73/i2/p91
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Russian version PDF:201
    English version PDF:10
    References:89
    First page:13
     
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