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On the Nikol’skii and Potapov classes of functions

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Abstract

It is proved that the Nikol’skii classes H 1 r and Potapov classes A 1 r contain the class W 1 r for r > 1/2.

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References

  1. M. K. Potapov, “On Jackson type theorems in the L p metric,” Dokl. Akad. Nauk SSSR 111 (6), 1185–1188 (1956).

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  2. M. K. Potapov, “On the approximation of nonperiodic functions by algebraic polynomials,” Vestn. Mosk. Univ., Ser. 1: Mat., Mekh., No. 4, 14–25 (1960).

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  3. M. K. Potapov, “On approximation by algebraic polynomials in the L p metric,” in Studies on Modern Problems of Constructive Function Theory (Fizmatgiz, Moscow, 1961), pp. 64–69 [in Russian].

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  4. V. P. Motornyi, “Approximation of functions by algebraic polynomials in the L p metric,” Izv. Akad. Nauk SSSR, Ser. Mat. 35 (4), 874–899 (1971) [Math. USSR, Izv. 5, 889–914 (1971)].

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Authors and Affiliations

  1. Oles Honchar Dnipropetrovsk National University, Gagarin Ave. 72, Dnipropetrovsk, 49010, Ukraine

    V. P. Motornyi

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  1. V. P. Motornyi
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Correspondence to V. P. Motornyi.

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Original Russian Text © V.P. Motornyi, 2016, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Vol. 293, pp. 224–235.

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Motornyi, V.P. On the Nikol’skii and Potapov classes of functions. Proc. Steklov Inst. Math. 293, 216–227 (2016). https://doi.org/10.1134/S0081543816040167

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  • DOI: https://doi.org/10.1134/S0081543816040167

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