Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces
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The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding Open image in new window fails for Open image in new window . 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.
KeywordsDifferential Equation Partial Differential Equation Ordinary Differential Equation Functional Equation Bounded Domain
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