Geodesic
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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 71-82

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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.
Mots-clés : Lebesgue function, orthogonal polynomials
Keywords: periodic weight. 
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     title = {Estimates of the {Lebesgue} function of {Fourier} sums over trigonometric polynomials orthogonal with a~weight not belonging to the spaces $L^r$ $(r>1)$},
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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 Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 71-82. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a9/