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Sharp Constants of Approximation Theory. II. Invariance Theorems and Certain Multivariate Inequalities of Different Metrics

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Abstract

We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov–Bernstein–Nikolskii type inequalities with the polyharmonic operator for algebraic polynomials on the unit sphere and the unit ball in \({\mathbb {R}}^m\) and the corresponding constants for entire functions of spherical type on \({\mathbb {R}}^m\). Certain relations in the univariate weighted spaces are discussed as well.

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Acknowledgements

We are grateful to both anonymous referees for valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Hampton University, Hampton, VA, 23668, USA

    Michael I. Ganzburg

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  1. Michael I. Ganzburg
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Correspondence to Michael I. Ganzburg.

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Communicated by Doron S. Lubinsky.

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Ganzburg, M.I. Sharp Constants of Approximation Theory. II. Invariance Theorems and Certain Multivariate Inequalities of Different Metrics. Constr Approx 50, 543–577 (2019). https://doi.org/10.1007/s00365-019-09481-2

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  • DOI: https://doi.org/10.1007/s00365-019-09481-2

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