Sharp Constants of Brézis-Gallouët-Wainger Type Inequalities with a Double Logarithmic Term on Bounded Domains in Besov and Triebel-Lizorkin Spaces. (18th October 2010)

• Record Type: Journal Article
• Authors: Morii Morii, Kei Kei; Sato Sato, Tokushi Tokushi; Sawano Sawano, Yoshihiro Yoshihiro; Wadade Wadade, Hidemitsu Hidemitsu
• Other Names: Shakhmurov Shakhmurov Veli B. Veli B. Academic Editor.
• Is Part Of: Boundary value problems. Volume 2010(2010)
• Publication Date: 2010-10-18
• Subjects: Boundary value problems -- Periodicals; Boundary value problems; Electronic journals; Periodicals; 515.35
• DOI: 10.1155/2010/584521
• Languages: English
• ISSNs: 1687-2762

Abstract

Abstract : The present paper concerns the Sobolev embedding in the endpoint case. It is known that the embedding W 1, n ( ℝ n ) ↪ L ∞ ( ℝ n ) fails for n ≥ 2 . 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.