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Kolmogorov inequalities for the norms of the Riesz derivatives of functions of many variables

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Abstract

New sharp Kolmogorov-type inequalities for the norms of the Riesz derivatives ∥Dαf∥∞ of functions \( f\in {L}_{\infty, E}^{\nabla}\left({\mathrm{\mathbb{R}}}^m\right) \) are obtained. Some applications of obtained inequalities are investigated.

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Authors and Affiliations

  1. Oles Honchar Dnipro National University, Dnipro, Ukraine

    Nataliia V. Parfinovych

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  1. Nataliia V. Parfinovych
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Correspondence to Nataliia V. Parfinovych.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 14, No. 2, pp. 265–278 April–June, 2017.

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Parfinovych, N.V. Kolmogorov inequalities for the norms of the Riesz derivatives of functions of many variables. J Math Sci 229, 85–95 (2018). https://doi.org/10.1007/s10958-018-3663-x

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  • DOI: https://doi.org/10.1007/s10958-018-3663-x

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