this is my question:
Show that $\epsilon ||f||_{L^n(\Omega')}\leq \epsilon^{\frac{x}{n}}$, where $x$ is a positive number, using these two facts:
$\int_{\Omega}|f|^x\leq C $
$|f|\le\dfrac{C}{\epsilon}$ in $\Omega'$
with $\Omega'$ subset of $\Omega$.
I think that the trick is something like Holder inequality, but i can't state something useful.