This article is cited in 6 papers

On divergence of Fourier–Walsh series of bounded functions on sets of measure zero

V. M. Bugadze

Tbilisi Ivane Javakhishvili State University

Abstract: It is known that for an arbitrary number $p$, $1\leqslant p<\infty$, and any set of measure zero there exists a function in $L^p(0,\, 1)$ whose Fourier–Walsh–Paley series diverges on the set. In this paper we prove an analogous result in the case $p=\infty$ for Fourier–Walsh series (Fourier–Walsh–Paley series and Fourier–Walsh–Kaczmarz series).

UDC: 517.51

MSC: Primary 42C10; Secondary 42C25

Received: 14.03.1993

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:2, 365–372

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