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  • Research Article
  • Open Access

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

  • 1,
  • 2,
  • 3Email author and
  • 4
Boundary Value Problems20102010:584521

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

  • Received: 4 October 2009
  • Accepted: 12 October 2010
  • Published:

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.

Keywords

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

Publisher note

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Authors’ Affiliations

(1)
Heian Jogakuin St. Agnes' School, 172-2, Gochomecho, Kamigyo-ku, Kyoto 602-8013, Japan
(2)
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
(3)
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan
(4)
Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan

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