In this paper we prove the inequality $$\int_{\mathbb R^n}\mu_R(|x|)|u(x)|^pdx\leqslant M\left[\int_{\mathbb R^n}|\nabla u(x)|^p\omega(|x|)dx+\left|\int_{|x|=R}u(x)ds\right|^p\right],$$ where $\omega(|x|) > 0$ and $\mu_R(|x|) > 0$ are the weight functions, $R > 0$ is an arbitrary number. In doing so, we first show some ”two-sides” Hardy type inequalities.