$\Lambda(\Psi)$-Fluctuation and the Fourier-Walsh series of bounded functions

S. F. Lukomskii

Saratov State University named after N. G. Chernyshevsky

Abstract: We consider the questions of convergence of Fourier–Walsh series in Lorentz spaces. Some condition is given on a function $f$ sufficient for its Fourier–Walsh series to converge in the Lorentz spaces “near” $L_\infty$. We show that this result is sharp.

Keywords: Fourier–Walsh series, convergence, Lorentz spaces.

Received: 18.11.2005

 English version: Siberian Mathematical Journal, 2007, 48:4, 648–652

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