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Mat. Sb., 2009, Volume 200, Number 11, Pages 45–60 (Mi msb7510)  

This article is cited in 5 scientific papers (total in 5 papers)

Hardy-Littlewood theorem for trigonometric series with $\alpha$-monotone coefficients

M. I. Dyachenkoa, E. D. Nursultanovbc

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Kazakhstan Branch of Lomonosov Moscow State University
c L. N. Gumilev Eurasian National University

Abstract: The Hardy-Littlewood theorem is established for trigonometric series with $\alpha$-monotone coefficients. Inequalities of Hardy-Littlewood kind are proved. Examples of series demonstrating that the results obtained are sharp are constructed.
Bibliography: 15 titles.

Keywords: generalized monotone coefficients, Hardy-Littlewood theorem.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm7510

Full text: PDF file (515 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:11, 1617–1631

Bibliographic databases:

UDC: 517.52
MSC: 42A16
Received: 03.12.2008 and 13.04.2009

Citation: M. I. Dyachenko, E. D. Nursultanov, “Hardy-Littlewood theorem for trigonometric series with $\alpha$-monotone coefficients”, Mat. Sb., 200:11 (2009), 45–60; Sb. Math., 200:11 (2009), 1617–1631

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. I. Dyachenko, S. Tikhonov, “Trigonometric series with lacunary-monotone coefficients”, Eurasian Math. J., 3:2 (2012), 31–52  mathnet  mathscinet  zmath
    2. Liflyand E., Tikhonov S., “Two-sided weighted Fourier inequalities”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 11:2 (2012), 341–362  mathscinet  zmath  isi
    3. A. U. Bimendina, E. S. Smailov, “Fourier–Price coefficients of class GM and best approximations of functions in the Lorentz space $L_{p\theta}[0,1)$, $1<p<+\infty$, $1<\theta<+\infty$”, Proc. Steklov Inst. Math., 293 (2016), 77–98  mathnet  crossref  crossref  mathscinet  isi  elib
    4. Dyachenko M., Mukanov A., Nursultanov E., “a Boas-Type Theorem For Alpha-Monotone Functions”, Math. Scand., 120:1 (2017), 39–58  crossref  mathscinet  zmath  isi  elib  scopus
    5. D. G. Dzhumabaeva, M. I. Dyachenko, E. D. Nursultanov, “On convergence of multiple trigonometric series with monotone coefficients”, Siberian Math. J., 58:2 (2017), 205–214  mathnet  crossref  crossref  isi  elib  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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