let $p>1$, and $f$ is continuous and $\displaystyle\int_{0}^{+\infty}|f(t)|^p|dt$ is convergence,show that
$$\left(\int_{0}^{+\infty}\left(\dfrac{1}{x}\int_{0}^{x}|f(t)|dt\right)^pdx\right)^{\frac{1}{p}}\le\dfrac{p}{p-1}\left(\int_{0}^{+\infty}|f(t)|^pdt\right)^{\frac{1}{p}}$$