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Sibirskii Matematicheskii Zhurnal, 2007, Volume 48, Number 2, Pages 341–352 (Mi smj27)  
This article is cited in 1 scientific paper (total in 1 paper)

The Fourier–Walsh series of the functions absolutely continuous in the generalized restricted sense

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky
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Abstract: We consider the questions of convergence in Lorentz spaces for the Fourier–Walsh series of the functions with Denjoy integrable derivative. We prove that a condition on a function $f$ sufficient for its Fourier–Walsh series to converge in the Lorentz spaces “near” $L_\infty$ cannot be expressed in terms of the growth of the derivative $f'$.
Keywords: Fourier–Walsh series, convergence, Lorentz space, Denjoy integral.
Received: 22.11.2004
Revised: 29.06.2005
English version:
Siberian Mathematical Journal, 2007, Volume 48, Issue 2, Pages 273–282
DOI: https://doi.org/10.1007/s11202-007-0027-z
Bibliographic databases:
UDC: 517.518.362
Language: Russian
Citation: S. F. Lukomskii, “The Fourier–Walsh series of the functions absolutely continuous in the generalized restricted sense”, Sibirsk. Mat. Zh., 48:2 (2007), 341–352; Siberian Math. J., 48:2 (2007), 273–282
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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