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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 2, Pages 243–265 (Mi izv1556)  

This article is cited in 19 scientific papers (total in 20 papers)

On a problem of Littlewood

S. V. Konyagin

Abstract: The Littlewood conjecture is proved: for any integers $m_1,…,m_M$
$$ \int_{-\pi}^{\pi}|\sum_{j=1}^M\exp(im_jx)| dx\geqslant C\ln M, $$
where $C>0$ is an absolute constant.
Bibliography: 19 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:2, 205–225

Bibliographic databases:

Document Type: Article
UDC: 517.5
MSC: Primary 42A05; Secondary 42C20
Received: 04.11.1980

Citation: S. V. Konyagin, “On a problem of Littlewood”, Izv. Akad. Nauk SSSR Ser. Mat., 45:2 (1981), 243–265; Math. USSR-Izv., 18:2 (1982), 205–225

Citation in format AMSBIB
\by S.~V.~Konyagin
\paper On~a~problem of Littlewood
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 2
\pages 243--265
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 2
\pages 205--225

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    This publication is cited in the following articles:
    1. Szilárd Gy Révész, “Rearrangements of Fourier series”, Journal of Approximation Theory, 60:1 (1990), 101  crossref
    2. A. S. Belov, “On an extremal problem on the minimum of a trigonometric polynomial”, Russian Acad. Sci. Izv. Math., 43:3 (1994), 593–606  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. A. Karatsuba, “An estimate of the $L_1$-norm of an exponential sum”, Math. Notes, 64:3 (1998), 401–404  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. A. Yudin, “Integral Norms of Trigonometric Polynomials”, Math. Notes, 70:2 (2001), 275–282  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. S. V. Konyagin, M. A. Skopina, “Comparison of the $L^1$-Norms of Total and Truncated Exponential Sums”, Math. Notes, 69:5 (2001), 644–651  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. R. M. Trigub, “A Lower Bound for the $L_1$-norm of Fourier Series of Polynomial Type”, Math. Notes, 73:6 (2003), 900–903  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. S. V. Bochkarev, “Multiplicative Inequalities for the $L_1$ Norm: Applications in Analysis and Number Theory”, Proc. Steklov Inst. Math., 255 (2006), 49–64  mathnet  crossref  mathscinet  elib
    8. S. V. Bochkarev, “Multiplicative Bounds for $L_1$-Norms of Exponential Sums”, Journal of Mathematical Sciences, 155:1 (2009), 47–56  mathnet  crossref  mathscinet
    9. S. V. Konyagin, “On the convergence of greedy approximants of trigonometric Fourier series”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S155–S167  mathnet  crossref  isi  elib
    10. St. Petersburg Math. J., 21:3 (2010), 365–405  mathnet  crossref  mathscinet  zmath  isi
    11. MICHAŁWOJCIECHOWSKI, “The non-equivalence between the trigonometric system and the system of functions with pointwise restrictions on values in the uniform and L1 norms”, Math. Proc. Camb. Phil. Soc, 150:03 (2011), 561  crossref
    12. Tamás Erdélyi, Kaveh Khodjasteh, Lorenza Viola, “The Size of Exponential Sums on Intervals of the Real Line”, Constr Approx, 2011  crossref
    13. Sándor Krenedits, “Three-term idempotent counterexamples in the Hardy–Littlewood majorant problem”, Journal of Mathematical Analysis and Applications, 2011  crossref
    14. A. S. Belov, “On the asymptotic solution of one extremal problem related to nonnegative trigonometric polynomials”, J. Math. Sci., 209:1 (2015), 19–50  mathnet  crossref  mathscinet
    15. S. V. Bochkarev, “de la Vallée-Poussin means of Fourier series for the quadratic spectrum and for spectra with power-like density”, Russian Math. Surveys, 69:1 (2014), 119–152  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. S. V. Konyagin, I. D. Shkredov, “On the Wiener norm of subsets of $\mathbb Z_p$ of medium size”, J. Math. Sci., 218:5 (2016), 599–608  mathnet  crossref  mathscinet  zmath  elib  elib
    17. S. V. Konyagin, I. D. Shkredov, “A quantitative version of the Beurling-Helson theorem”, Funct. Anal. Appl., 49:2 (2015), 110–121  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. A. S. Belov, “Bound of remainder term of asymptotic solution one extremal problem connected with nonnegative trigonometric polynomials”, Math. Notes, 100:2 (2016), 325–329  mathnet  crossref  crossref  mathscinet  isi  elib
    19. Borodin P.A. Konyagin S.V., “Convergence to Zero of Exponential Sums With Positive Integer Coefficients and Approximation By Sums of Shifts of a Single Function on the Line”, Anal. Math., 44:2 (2018), 163–183  crossref  isi
    20. B. S. Kashin, Yu. V. Malykhin, V. Yu. Protasov, K. S. Ryutin, I. D. Shkredov, “Sergei Vladimirovich Konyagin turns 60”, Proc. Steklov Inst. Math., 303 (2018), 1–9  mathnet  crossref  crossref  isi  elib
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