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On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces

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Abstract

We present a unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Pólya and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp inequalities for the norms of powers of the Laplace-Beltrami operators on compact Riemannian manifolds and derive the well-known Taikov and Hardy-Littlewood-Pólya inequalities for functions defined on the d-dimensional space in the limit case. Other applications include the best approximation of unbounded operators by linear bounded ones and the best approximation of one class by elements of another class. In addition, we establish sharp Solyar type inequalities for unbounded closed operators with closed range.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Oles Honchar Dnipro National University, Gagarina pr. 72, 49010, Dnipro, Ukraine

    V. Babenko, N. Kriachko & D. Skorokhodov

  2. Department of Mathematics, Kennesaw State University, 1100 South Marietta Pkwy, Marietta, GA, 30060, U.S.A.

    Yu. Babenko

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  1. V. Babenko
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  2. Yu. Babenko
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  3. N. Kriachko
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  4. D. Skorokhodov
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Correspondence to D. Skorokhodov.

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This work was supported by Simons Collaboration Grant No. 210363.

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Babenko, V., Babenko, Y., Kriachko, N. et al. On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces. Anal Math 47, 709–745 (2021). https://doi.org/10.1007/s10476-021-0104-8

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  • DOI: https://doi.org/10.1007/s10476-021-0104-8

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