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Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces

Abstract

The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding fails for . Brézis-Gallouët-Wainger and some other authors quantified why this embedding fails by means of the Hölder-Zygmund norm. In the present paper we will give a complete quantification of their results and clarify the sharp constants for the coefficients of the logarithmic terms in Besov and Triebel-Lizorkin spaces.

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Correspondence to Yoshihiro Sawano.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Morii, K., Sato, T., Sawano, Y. et al. Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces. Bound Value Probl 2010, 584521 (2010). https://doi.org/10.1155/2010/584521

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  • DOI: https://doi.org/10.1155/2010/584521

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Bounded Domain