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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

Boundary Value Problems volume 2010, Article number: 584521 (2010) Cite this article

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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Authors and Affiliations

  1. Heian Jogakuin St. Agnes' School, 172-2, Gochomecho, Kamigyo-ku, Kyoto, 602-8013, Japan

    Kei Morii

  2. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

    Tokushi Sato

  3. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Yoshihiro Sawano

  4. Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Hidemitsu Wadade

Authors
  1. Kei Morii
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  2. Tokushi Sato
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  3. Yoshihiro Sawano
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  4. Hidemitsu Wadade
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Corresponding author

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