Geodesic
On divergence of Fourier--Walsh series of bounded functions on sets of measure zero
Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 365-372

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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). 
@article{SM_1995_82_2_a7,
     author = {V. M. Bugadze},
     title = {On divergence of {Fourier--Walsh} series of bounded functions on sets of measure zero},
     journal = {Sbornik. Mathematics},
     pages = {365--372},
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     volume = {82},
     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_82_2_a7/}
}
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V. M. Bugadze. On divergence of Fourier--Walsh series of bounded functions on sets of measure zero. Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 365-372. http://geodesic.mathdoc.fr/item/SM_1995_82_2_a7/