New characterization of Morrey spaces

In this paper we prove that the norm of the Morrey space $\mathcal{M}_{p,\lambda}$ is equivalent to
$$ \sup\left\{\int_{\mathbb{R}^n}|fg|: \inf_{x\in\mathbb{R}^n}\int_0^\infty r^{\frac{n-\lambda}p-1}||g||_{L_{p'}(^\complement B(x,r))}dr\leqslant1\right\}. $$