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Trudy Instituta Matematiki i Mekhaniki 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
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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.
Received: 30.03.2011
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, Volume 277, Issue 1, Pages 21–32
DOI: https://doi.org/10.1134/S0081543812050045
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
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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\pages 71--82
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    • This publication is cited in the following 1 articles:
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