$$\bex q>3\ra \sen{\n f}_{L^\infty} \leq C(q)\sez{ 1+\sen{\n f}_{BMO} \ln^\frac{1}{2}\sex{e+\sen{\n f}_{W^{1,q}}+\sen{f}_{L^\infty}} }. \eex$$ $$\bex m\geq 3\ra \sen{\n f}_{L^\infty}\leq C\sez{ 1+\sen{\n f}_{BMO} \ln^\frac{1}{2} \sex{1+\sen{\n f}_{H^m}} }. \eex$$ see [D. Chae, J. Lee, On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics, J. Differential Equations, 256 (2014), 3835--3858].
[再寄小读者之数学篇](2014-06-26 Logarithmical Sobolev inequality using BMO space),布布扣,bubuko.com
[再寄小读者之数学篇](2014-06-26 Logarithmical Sobolev inequality using BMO space)
原文地址：http://www.cnblogs.com/zhangzujin/p/3810880.html
