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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 3, Pages 71–82 (Mi timm722)  

This article is cited in 1 scientific paper (total in 1 paper)

Estimates of the Lebesgue function of Fourier sums over trigonometric polynomials orthogonal with a weight not belonging to the spaces $L^r$ $(r>1)$

V. M. Badkovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

Abstract: A two-sided pointwise estimate is obtained for the Lebesgue function of Fourier sums with respect to trigonometric polynomials orthogonal with a $2\pi$-periodic weight that differs from the function $1/|\sin(\tau/2)|$ by some factor slowly changing at zero. The weight under consideration does not belong to the space $L^r$ for any $r>1$. A similar result for polynomials orthogonal on the interval $[-1,1]$ is obtained in the form of a corollary.

Keywords: Lebesgue function, orthogonal polynomials, periodic weight.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 277, suppl. 1, 21–32

Bibliographic databases:

UDC: 517.5
Received: 30.03.2011

Citation: V. M. Badkov, “Estimates of the Lebesgue function of Fourier sums over trigonometric polynomials orthogonal with a weight not belonging to the spaces $L^r$ $(r>1)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 3, 2011, 71–82; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 21–32

Citation in format AMSBIB
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\by V.~M.~Badkov
\paper Estimates of the Lebesgue function of Fourier sums over trigonometric polynomials orthogonal with a~weight not belonging to the spaces $L^r$ $(r>1)$
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 3
\pages 71--82
\mathnet{http://mi.mathnet.ru/timm722}
\elib{http://elibrary.ru/item.asp?id=17870122}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2012
\vol 277
\issue , suppl. 1
\pages 21--32
\crossref{https://doi.org/10.1134/S0081543812050045}
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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. I. A. Shakirov, “On two-sided estimate for norm of Fourier operator”, Ufa Math. J., 10:1 (2018), 94–114  mathnet  crossref  isi  elib
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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