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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

  • Kei Morii1,
  • Tokushi Sato2,
  • Yoshihiro Sawano3Email author and
  • Hidemitsu Wadade4
Boundary Value Problems20102010:584521

Received: 4 October 2009

Accepted: 12 October 2010

Published: 18 October 2010


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.


Differential EquationPartial Differential EquationOrdinary Differential EquationFunctional EquationBounded Domain

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Authors’ Affiliations

Heian Jogakuin St. Agnes' School, Kyoto, Japan
Mathematical Institute, Tohoku University, Sendai, Japan
Department of Mathematics, Kyoto University, Kyoto, Japan
Department of Mathematics, Osaka City University, Osaka, Japan


© 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.