References
B. Aubertin and J. J. F. Fournier, An integrability theorem for unbounded Vilenkin systems, to appear.
J. A. Chao, Hardy spaces on regular martingales, Martingale Theory in Harmonic Analysis, Springer (Berlin, 1981); also known as Lecture Notes in Mathematics, 939 (1981), 18–28.
J. J. F. Fournier, On a theorem of Paley and the Littlewood conjecture, Arkiv för mat., 17 (1979), 199-216.
J. J. F. Fournier, Some remarks on the recent proofs of the Littlewood conjecture, Canadian Math. Soc. Conference Proceedings, 3 (1983), 157-170.
S. Fridli and P. Simon, On the Dirichlet kernels and a Hardy space with respect to the Vilenkin system, Acta. Math. Hungar., 45 (1985), 223-234.
B. Golubov, A. Efimov, and V. Skvortsov, Walsh Series and Transforms, Kluwer Academic Publisher (Dordrecht, The Netherlands, 1991).
O. C. McGehee, L. Pigno, and B. Smith, Hardy's inequality and the L 1 norm of exponential sums, Annals of Math., 113 (1981), 613-618.
L. Pigno and B. Smith, A Littlewood-Paley inequality for analytic measures, Ark. för Mat., 20 (1982), 271-274.
W. Rudin, Remarks on a theorem of Paley, J. London Math. Soc., 32 (1960), 307-311.
P. Simon, On the concept of conjugate function, Colloq. Math. Soc. János Bolyai, 19 (1976), 747-755; also known as Fourier Analysis and Approximation Theory (Budapest, 1976).
P. Simon, Investigations with respect to the Vilenkin system, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 28 (1985), 87-101.
W. R. Wade, Vilenkin-Fourier series and approximation, Colloquia. Math. Soc. János Bolyai, 58, 699-734; Approximation Theory (Kecskemét, Hungary, 1990). edited by J. Szabados and K. Tandori, North Holland (Amsterdam, New York, 1991).
W. R. Wade, Review of [6], Bull. Amer. Math. Soc., 26 (1992), 348-359.
F. Weisz, Conjugate martingale transforms, Studia Math., 103 (1992), 205-220.
F. Weisz, Martingale Hardy Spaces and Their Applications in Fourier Analysis, Lecture Notes in Mathematics, 1568, Springer-Verlag (Berlin, New York, 1994).
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Fournier, J.J.F. Hardy and Paley Inequalities for Fully-Odd Vilenkin Systems. Acta Mathematica Hungarica 75, 89–103 (1997). https://doi.org/10.1023/A:1006534802172
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DOI: https://doi.org/10.1023/A:1006534802172