Boundary Value Problems

, 2010:584521 | Cite as

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

  • Kei Morii
  • Tokushi Sato
  • Yoshihiro Sawano
  • Hidemitsu Wadade
Open Access
Research Article

Abstract

The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding Open image in new window fails for Open image in new window . 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 

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Copyright information

© Kei Morii et al. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Kei Morii
    • 1
  • Tokushi Sato
    • 2
  • Yoshihiro Sawano
    • 3
  • Hidemitsu Wadade
    • 4
  1. 1.Heian Jogakuin St. Agnes' SchoolKyotoJapan
  2. 2.Mathematical InstituteTohoku UniversitySendaiJapan
  3. 3.Department of MathematicsKyoto UniversityKyotoJapan
  4. 4.Department of MathematicsOsaka City UniversityOsakaJapan

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