Title: Brézis–Gallouët–Wainger type inequality with a double logarithmic term in the Hölder space: Its sharp constants and extremal functions
Abstract: We investigate the sharp constants in a Brezis-Gallouet-Wainger type inequality with a double logarithmic term in the Holder space in a bounded domain in R n . Ibrahim, Majdoub and Masmoudi gave the sharp constant in the 2-dimensional case. We make precise estimates to give the sharp constants, and pass to the case of higher dimensions n ‚ 2. We can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball. 2000 Mathematics Subject Classification. Primary 46E35; Secondary 35J85.