RESUMEN

In[9], Zhu proved that if f holomorphic in the unit ball B of Cⁿ, then f ε L^p (B, dv) if all the functions (1 -|x|²)^m(D^αf)(z) with |α| = m are in L^p(B, dv). His method  can only deal with the case of p≥1. in this paper, we give a new approach which is completely different from that of [9] to prove that the above result Lodz for all p ε (0.∞). A simple proof. About hte charcterization of  the Bloch space Hill be given. As a by-product of our approach, we generalize a theorem in [4] to the unit ball of Cⁿ, and use this result to gereralize some theorems about the pluriharmonic conjugates in [7] and [2] to the case 0 < p <1.