The closure of derivative average radial integrable spaces in the Bloch space

A description of the closure in the Bloch space of the Bloch functions that are in the derivative average radial integrable space is given. As a byproduct, we get some new characterizations for the Bloch space $\mathcal{B}$ $\mathcal{B}$ , the little Bloch space ${\mathcal{B}}_0$ $\mathcal{B}_{0}$ , and the closure of the space $H^2\cap \mathcal{B}$ $H^{2}\cap \mathcal{B}$ in the Bloch norm.