Hölder's inequality aplication

Question

I have to do this exercise: Let $f\in{L^{p}([0,1])}$, with $1<p<+\infty$. Prove that $\lim\limits_{j\to\infty} {j^{(2p-2)/p}}\left| \int_{1/(j+1)}^{1/j} {f}\mathrm{d}m\right\| =0$. I don't know how to use the Hölder inequality to solve the exercise.