This article is cited 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

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.

UDC: 517.518.362

Received: 22.11.2004
Revised: 29.06.2005

 English version: Siberian Mathematical Journal, 2007, 48:2, 273–282

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