Brezis-Gallouet-Wainger type inequality with critical fractional Sobolev space and BMO

Abstract

In this paper, we prove the Brezis-Gallouet-Wainger type inequality involving the BMO norm, the fractional Sobolev norm, and the logarithmic norm of $\mathcal{\dot{C}}^\eta$, for $\eta\in(0,1)$.