Sobolev's imbedding theorem in the limiting case with Lorentz space and BMO

Kozono, Hideo; Minamidate, Kouei; Wadade, Hidemitsu

doi:10.2969/aspm/04710159

VOL. 47.1 | 2007 Sobolev's imbedding theorem in the limiting case with Lorentz space and BMO

Chapter Author(s) Hideo Kozono, Kouei Minamidate, Hidemitsu Wadade

Editor(s) Hideo Kozono, Takayoshi Ogawa, Kazunaga Tanaka, Yoshio Tsutsumi, Eiji Yanagida

Adv. Stud. Pure Math., 2007: 159-167 (2007) DOI: 10.2969/aspm/04710159

Abstract

We shall prove a Gagliardo-Nirenberg type interpolation inequality with Lorentz space and BMO of functions of bounded mean oscillation in the critical case. Moreover, we obtain a Trudinger type inequality and a Brezis-Gallouet-Wainger type inequality as an application of the Gagliardo-Nirenberg type inequality.