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Exact Constants for Simultaneous Approximation of Sobolev Classes by Piecewise Hermite Interpolation

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Abstract

We determine the exact constants for simultaneous L2-approximation of Sobolev classes by piecewise Hermite interpolation with equidistant nodes. The general results are applied to obtain sharp Wirtinger–Sobolev type inequalities.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Normal University, Tianjin, 300387, P. R. China

    G. Q. Xu & L. Y. Xiong

  2. Department of Mathematics, Beijing Normal University, Beijing, 100875, P. R. China

    Y. P. Liu

Authors
  1. G. Q. Xu
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  2. Y. P. Liu
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  3. L. Y. Xiong
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Correspondence to G. Q. Xu.

Additional information

Supported by National Natural Science Foundation of China (Project No. 11471043, 11671271), and by Beijing Natural Science Foundation (Project No. 1132001).

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Xu, G.Q., Liu, Y.P. & Xiong, L.Y. Exact Constants for Simultaneous Approximation of Sobolev Classes by Piecewise Hermite Interpolation. Anal Math 45, 621–645 (2019). https://doi.org/10.1007/s10476-019-0985-y

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  • DOI: https://doi.org/10.1007/s10476-019-0985-y

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