Zygmund Type Mean Lipschitz Spaces on the Unit Ball of ℂ n

Abstract

On the unit ball of ℂ n , the space of those holomorphic functions satisfying mean Lipschitz condition $$ \int_0^1 \omega^*_p(t, f)^q \frac{dt}{t^{1+ q}} <\infty$$ is characterized by integral growth conditions of the tangential derivatives as well as the radial derivatives, where $\omega^*_p(t, f)$ denotes the double difference L p modulus of continuity defined in terms of the unitary transformations of ℂ n .