Abstract
We consider the questions of convergence of Fourier-Walsh series in Lorentz spaces. Some condition is given on a function ƒ sufficient for its Fourier-Walsh series to converge in the Lorentz spaces “near” L ∞. We show that this result is sharp.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 4, pp. 811–816, July–August, 2007.
Original Russian Text Copyright © 2007 Lukomskiĭ S. F.
The author was supported by the Russian Foundation for Basic Research (Grant 03-01-00390).
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Lukomskii, S.F. Λ(Ψ)-Fluctuation and the Fourier-Walsh series of bounded functions. Sib Math J 48, 648–652 (2007). https://doi.org/10.1007/s11202-007-0066-5
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DOI: https://doi.org/10.1007/s11202-007-0066-5