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Nikol’skii Inequality Between the Uniform Norm and Integral Norm with Bessel Weight for Entire Functions of Exponential Type on the Half-Line

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Abstract

We study a Nikol’skii type inequality for even entire functions of given exponential type between the uniform norm on the half-line [0,∞) and the norm (∫ ∞0 |f(x)|qx2α+1dx)1/q of the space Lq((0,∞), x2α+1) with the Bessel weight for 1 ≤ q < ∞ and α > −1/2. An extremal function is characterized. In particular, we prove that the uniform norm of an extremal function is attained only at the end point x = 0 of the half-line. To prove these results, we use the Bessel generalized translation.

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Authors and Affiliations

  1. Institute of Natural Sciences and Mathematics, Ural Federal University, Yekaterinburg, Russia

    V. Arestov, A. Babenko & M. Deikalova

  2. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia

    V. Arestov, A. Babenko & M. Deikalova

  3. Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary

    Á. Horváth

Authors
  1. V. Arestov
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  2. A. Babenko
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  3. M. Deikalova
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  4. Á. Horváth
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Corresponding author

Correspondence to M. Deikalova.

Additional information

This work was supported by the Russian Academic Excellence Project (agreement no. 02.A03.21.0006 of August 27, 2013, between the Ministry of Education and Science of the Russian Federation and Ural Federal University).

V. Arestov, A. Babenko and M. Deikalova were supported by the Russian Foundation for Basic Research (project no. 18-01-00336).

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Arestov, V., Babenko, A., Deikalova, M. et al. Nikol’skii Inequality Between the Uniform Norm and Integral Norm with Bessel Weight for Entire Functions of Exponential Type on the Half-Line. Anal Math 44, 21–42 (2018). https://doi.org/10.1007/s10476-018-0103-6

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  • DOI: https://doi.org/10.1007/s10476-018-0103-6

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