Geodesic
On approximation of functions by singular integrals in the Hausdorff metric
Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 229-246 
A. P. Petukhov. On approximation of functions by singular integrals in the Hausdorff metric. Sbornik. Mathematics, Tome 63 (1989) no. 1, pp. 229-246. http://geodesic.mathdoc.fr/item/SM_1989_63_1_a15/
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     title = {On approximation of functions by singular integrals in the {Hausdorff} metric},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_63_1_a15/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions are found for convergence in the Hausdorff metric of a sequence of integral operators on an arbitrary bounded measurable function. The criterion obtained is used to investigate summation of trigonometric Fourier series by the Abel–Poisson, Vallée-Poussin, Bernstein–Rogosinski, and Cesàro methods. Bibliography: 7 titles.

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[2] Lebesgue H., “Sur les integrates singulieres”, Ann. Toulouse, 1 (1909), 25–117 | MR

[3] Fikhtengolts G. M., Teoriya prostykh opredelennykh integralov, zavisyaschikh ot parametra, Petrograd, 1918

[4] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974 | MR

[5] Natanson G. I., “Yavlenie Gibbsa dlya summ Valle-Pussena”, Issledovaniya po sovremennym problemam konstruktivnoi teorii funktsii, GIFML, M., 1961, 206–213 | MR

[6] Kharshiladze F. I., “Yavlenie Gibbsa pri summirovanii ryada Fure metodami Bernshteina–Rogozinskogo”, DAN SSSR, 101:3 (1955), 425–428

[7] Zigmund A., Trigonometricheskie ryady, Mir, M., 1965 | MR