The diagonal mapping in general Hardy spaces in the polidisk

For $p=(p_1,p_2)$, $1<p_i<+\infty$, $i=1,2$, let $H^{p_1,p_2}$ be the Hardy class on the bidisk with mixed norm. We give a complete discription of all holomorphic function $\varphi$ in the unit disk that are representable in the form $\varphi(z)=f(z,z)$, $|z|<1$, with $f\in H^{p_1,p_2}$.