Characterizations of spaces in the unit ball of

Let B denote the unit ball of C n . For 0 < p < ∞ , the holomorphic function spaces Q p and Q p , 0 on the unit ball of C n are defined as f ∈ Q p ⇔ sup a ∈ B ∫ B | ∇ ˜ f ( z ) | 2 G p ( z , a ) d λ ( z ) < ∞ and f ∈ Q p , 0 ⇔ lim | a | → 1 ∫ B | ∇ ˜ f ( z ) | 2 G p ( z , a ) d λ ( z ) = 0 . In this paper, we give some derivative-free, mixture and oscillation characterizations for Q p and Q p , 0 spaces in the unit ball of C n .