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Open Access Research Article

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 Sawano3* and Hidemitsu Wadade4

Author 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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Boundary Value Problems 2010, 2010:584521  doi:10.1155/2010/584521


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2010/1/584521


Received:4 October 2009
Revisions received:15 September 2010
Accepted:12 October 2010
Published:18 October 2010

© 2010 Kei Morii et al.

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.

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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