An inequality of Paley and convergence a.e. of Walsh-Fourier series
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Hunt, R. A., On the convergence of Fourier series. Orthogonal expansions and their continuous analogues. SIU Press, Carbondale, Illinois, 1968. (To appear).
Paley, R. E. A. C., A remarkable series of orthogonal functions (I). Proc. London Math. Soc.34, 241–264 (1932).
Zygmund, A., Trigonometric series, vol. II, 1959.