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 ∞ cannot be expressed in terms of the growth of the derivative f′.
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Original Russian Text Copyright © 2007 Lukomskiĭ S. F.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 2, pp. 341–352, March–April, 2007.
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Lukomskii, S.F. The Fourier-Walsh series of the functions absolutely continuous in the generalized restricted sense. Sib Math J 48, 273–282 (2007). https://doi.org/10.1007/s11202-007-0027-z
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DOI: https://doi.org/10.1007/s11202-007-0027-z