Skip to main content

Advertisement

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

Article metrics

  • 909 Accesses

  • 4 Citations

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.

Publisher note

To access the full article, please see PDF.

Author information

Correspondence to Yoshihiro Sawano.

Rights and permissions

Reprints and Permissions

About this article

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Bounded Domain