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
- Kei Morii1,
- Tokushi Sato2,
- Yoshihiro Sawano3Email author and
- Hidemitsu Wadade4
Received: 4 October 2009
Accepted: 12 October 2010
Published: 18 October 2010
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’ Affiliations
(1)
Heian Jogakuin St. Agnes' School
(2)
Mathematical Institute, Tohoku University
(3)
Department of Mathematics, Kyoto University
(4)
Department of Mathematics, Osaka City University
Copyright
© 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.
