An inequality of Paley and convergence a.e. of Walsh-Fourier series

Arkiv för Matematik - Tập 7 Số 6 - Trang 551-570 - 1969
Per Sjölin1
1Department of Mathematics, University of Uppsala, Uppsala, Sweden

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Tài liệu tham khảo

Billard, P., Sur la convergence presque partout des séries de Fourier Walsh des fonctions de l’espaceL 2(0, 1). Studia Math. 28, 363–388 (1967).

Carleson, L., On convergence and growth of partial sums of Fourier series. Acta Math.116, 135–157 (1966).

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).

Phillips, K., The maximal theorems of Hardy and Littlewood. Amer. Math. Monthly74, 648–660 (1967).

Watari, C., Mean convergence of Walsh-Fourier series. Tôhoku Math. J. (2) 16, 183–188 (1964).

Zygmund, A., Trigonometric series, vol. II, 1959.