I am looking for a reference or a direct argument that shows the real interpolation space between $L_p$ and $B^s_{q,q}$ is $B^\alpha_{r,r}$, with the usual conditions on the indices. This result is stated in many places, and they refer to, e.g., a paper of DeVore and Popov on interpolation of Besov spaces, but this paper is concerned with only interpolation between two Besov spaces. When I try to replace one of the Besov spaces by an $L_p$ space, I run into the problem that $L_p$ spaces are not of the correct $\ell_q^s(L_p)$-type. I might be missing some simple argument. I would really appreciate if you give me some pointer.