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An estimate of an optimal argument in the sharp multidimensional Jackson-Stechkin L 2-inequality

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Abstract

An estimate of an optimal argument in the sharp Jackson-Stechkin inequality in the space L 2(ℝn) is proved in the case of a generalized modulus of continuity; its special case is the classical modulus of continuity. Similar statements hold for the torus \(\mathbb{T}^n \). The obtained results agree with Chernykh’s classical one-dimensional theorems and refine some results by S.N. Vasil’ev, A.I. Kozko, and A.V. Rozhdestvenskii.

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Authors and Affiliations

  1. Tula State University, pr. Lenina 92, Tula, 300600, Russia

    D. V. Gorbachev

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  1. D. V. Gorbachev
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Correspondence to D. V. Gorbachev.

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Original Russian Text © D.V.Gorbachev, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 1.

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Gorbachev, D.V. An estimate of an optimal argument in the sharp multidimensional Jackson-Stechkin L 2-inequality. Proc. Steklov Inst. Math. 288 (Suppl 1), 70–78 (2015). https://doi.org/10.1134/S008154381502008X

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