Geodesic
Examples of divergent Fourier series for a wide class of rearranged Walsh–Paley system
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 3-8
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A rearranged Walsh system is considered in the paper. An example of a Fourier series from the class $Lo(\sqrt{\ln^{+}})L$ divergent almost everywhere is constructed. 
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I. V. Polyakov. Examples of divergent Fourier series for a wide class of rearranged Walsh–Paley system. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2012), pp. 3-8. http://geodesic.mathdoc.fr/item/VMUMM_2012_6_a0/

[1] Carleson L., “On the convergence and growth of partial sums of Fourier series”, Acta. Math., 116 (1966), 135–157 | DOI | MR

[2] Kolmogoroff A.N., “Une serie de Fourier–Lebesgue divergente partout”, C.r. Acad. sci. Paris, 183 (1926), 1327–1329

[3] Antonov N.Y., “Convergence of Fourier series”, East J. Approx., 2:2 (1996), 187–196 | MR

[4] Sjolin P., Soria F., “Remarks on theorem by N. Y. Antonov”, Stud. Math., 158 (2003), 79–97 | DOI | MR

[5] Konyagin S.V., “O raskhodimosti vsyudu trigonometricheskikh ryadov Fure”, Matem. sb., 191:1 (2000), 103–126 | DOI | MR

[6] Bochkarev S.V., “Vsyudu raskhodyaschiesya ryady Fure po sisteme Uolsha i multiplikativnym sistemam”, Uspekhi matem. nauk, 59:1(355) (2004), 103–124 | DOI | MR

[7] Moon K., “An everywhere divergent Fourier–Walsh series of the class $ L (\ln^{+} \ln^{+})^{1 - \epsilon } L $”, Proc. Amer. Math. Soc., 50 (1975), 309–314 | MR

[8] Balashov L.A., “O ryadakh po sisteme Uolsha s monotonnymi koeffitsientami”, Sib. matem. zhurn., 12:1 (1971), 25–39

[9] Schipp F., “Nekotorye perestanovki sistemy Uolsha”, Matem. zametki, 18 (1975), 193–201 | MR

[10] Schipp F., Wade W.R., Simon P., Walsh series. An introduction to dyadic harmonic analysis, Budapest, 1990 | MR

[11] Golubov B.I., Efimov A.V., Skvortsov V.A., Ryady i preobrazovaniya Uolsha. Teoriya i primeneniya, Nauka, M., 1987 | MR

[12] Petrov V.V., Predelnye teoremy dlya summ nezavisimykh sluchainykh velichin, Nauka, M., 1987 | MR