Abstract
A solution of the recently-resolved Littlewood conjecture is here presented in two stages of proof: the development of one-sided Riesz products and the Littlewood-product construction. In addition, problems are listed having to do with exerting more control on drift damage, with filling in gaps in our knowledge of trigonometric designs, and with positive mass interpolation vs. the sup interpolations of the present paper.
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References
P. Cohen, On a conjecture of Littlewood and idempotent measures. Amer. J. Math. 82 (1960), 191–212.
H. Davenport, On a theorem of P.J. Cohen. Mathematika 7 (1960), 93–97.
J.J.F. Fournier, On a theorem of Paley and the Littlewood conjecture. Arkiv for Mathematik 17 (1979), 199–216.
G.H. Hardy and J.E. Littlewood, A new proof of a theorem on rearrangements. J. London Math. Soc. 23 (1918), 163–168.
S.B, Konyagin, On a problem of Littlewood. Izvestia, 1981.
O.C. McGehee, L. Pigno, and B. Smith, Hardy’s inequality and the L1 norm of exponential sums. Ann, of Math. 113 (1981), 613–618.
S.K. Pichorides, On the L1 norm of exponential sums. Ann. Inst. Fourier, Grenoble 30, 2 (1980), 79–89.
S.K. Pichorides, Lp norms of exponential sums. Publications mathematiques d’ORSAY, No. 77-73, 1977.
S.K. Pichorides, On a conjecture of Littlewood. To appear in Math. Intelligencer.
J.D. Stegeman, On the best constant in the Littlewood problem. University Utrecht, preprint no. 232.
S.J. Szarek and T. Wolniewicz, A proof of Fefferman’s theorem on multipliers. Polish Academy of Sciences, preprint.
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© 1983 Springer Basel AG
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Smith, B. (1983). Two Trigonometric Designs: One-Sided Riesz Products and Littlewood Products. In: Beckenbach, E.F., Walter, W. (eds) General Inequalities 3. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 64. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6290-5_9
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DOI: https://doi.org/10.1007/978-3-0348-6290-5_9
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