Search for a reference on characterising Lebesgue spaces in terms of (inhomogeneous) Besov spaces.

Question

I am trying to find a proof that

$||f||_{L^{p}}\sim{}||f||_{B^0_{p,2}}$

where $||f||_{B^s_{p,r}}=||(2^{js}||f_j||_{L^p})_{j\in\mathrm{Z}_{\geq{}-1}}||_{\ell^r}$ is the norm characterising the inhomogeneous Besov space. (Here $f=\sum{}f_j$ is the Littlewood-Paley decomposition.) Any references would be greatly appreciated.