For $f\in H^s(\bbR^3)$ with $s>\cfrac{3}{2}$, we have $$\bex \sen{f}_{L^\infty}\leq C\sex{1+\sen{f}_{\dot B^0_{\infty,\infty}}}\ln \sex{1+\sen{f}_{H^s}},\quad s>\cfrac{3}{2}. \eex$$ see [D. Chae, P. Degond, J.G. Liu, Well-posedness for Hall-magnetohydrodynamics, Ann. I. H. Poincar\'e-AN, 31 (2014),555--565].