- 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 Morii et al. 2010
- 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 Equation
- Partial Differential Equation
- Ordinary Differential Equation
- Functional Equation
- Bounded Domain
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