  The main result of this paper is related to finding two-sided bounds of norm
for the adjoint operator $P^{\ast}$ of the Bergman projection $P,$ where $P$
denotes the Bergman projection wich maps $L^{1}(D,d\lambda(z))$ onto the Besov
space $B_{1}.$ Here $d\lambda(z)$ is the M\"obius invariant measure
${(1-|z|^2)^{-2}}{dA(z)}$. It is shown that $2\leq\| P^{\ast}\|\leq 4.$
