On the unit ball of $mathbb{C}^n$, the space of those holomorphic functions satisfying the mean Lipschitz condition $${int}_0^1;{omega}_p(t,f)^qfrac{dt}{t^1+{alpha}q};<;{infty}$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where ${omega}_p(t,f)$ denotes the $L^p$ modulus of continuity defined in terms of the unitary transformations of $mathbb{C}^n$.