Abstract
For trigonometric polynomials with coefficients equal to 1 or 0 in absolute value whose spectra are located on the left-hand side of binary blocks, we establish two-sided estimates of the L 1-norm.
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REFERENCES
S. V. Konyagin, “On the Littlewood problem,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 45 (1981), no. 2, 243–265.
O. C. McGehee, L. Pigno, and B. Smith, “Hardy's inequality and the L1-norm of exponential sums,” Ann. of Math., 113 (1981), no. 3, 613–618.
S. V. Bochkarev, “On a method for estimating the L1-norm of an exponential sum,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 218 (1997), 74–76.
M. Weiss, “A theorem on lacunary trigonometric series,” in: Orthogonal Expansions and Their Continuous Analogues, Proc. Conf. South. III Univ. (Edwardsville, 1967), SIU Press, Carbondale, Illinois, 1968, pp. 227–230.
L. A. Balashov and S. A. Telyakovskii, “Some properties of lacunary series and the integrability of trigonometric series,” Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 143 (1977), 32–41.
B. Smith, “Two trigonometric designs:one-sided Riesz products and Littlewood products,” in: General Inequalities 3, vol. 64, Intern. Series of Numer. Math, Birkhäuser, Basel, 1983, pp. 141–148.
A. Zygmund, Trigonometric Series, vol. 1, Cambridge Univ. Press, Cambridge, 1959.
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Yudin, V.A. Integral Norms of Trigonometric Polynomials. Mathematical Notes 70, 275–282 (2001). https://doi.org/10.1023/A:1010219228386
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DOI: https://doi.org/10.1023/A:1010219228386