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

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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Affiliations

1. Heian Jogakuin St. Agnes' School, 172-2, Gochomecho, Kamigyo-ku, Kyoto, 602-8013, Japan

   • Kei Morii

2. Mathematical Institute, Tohoku University, Sendai, 980-8578, Japan

   • Tokushi Sato

3. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

   • Yoshihiro Sawano

4. Department of Mathematics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

   • Hidemitsu Wadade

Corresponding author

Correspondence to Yoshihiro Sawano.

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