Here $B\_r$ presents the open ball of radius r in $R^3$. So I hope to know how to prove the following inequality.
$$
\int\_{B\_r} |u|\le Cr^{\frac{9}{5}}\left(\int\_{B\_r} |u|^2\right)^{\frac{1}{5}}\left(\int\_{B\_r} |u|^3\right)^{\frac{1}{5}}
$$
I did not figure out where these exponents come from. Could anyone show me?



Using Hölder's Inequality to prove the following equation
I think that I have got the answer… it is quite a simple result from the Hölder inequality,
$u^{\frac{2}{5}}u^{\frac{3}{5}}1$ with exponents $\frac{1}{5}$, $\frac{1}{5}$ and $\frac{3}{5}$….


