Hyperbolic mean growth of bounded holomorphic functions in the ball

摘要

We consider the hyperbolic Hardy class rhoH(p)(B), 0 < p < infinity. It consists of phi holomorphic in the unit complex ball B for which phi < 1 and [GRAPHICS] where ρ denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type g-function and the area function are defined in terms of the invariant gradient of B, and membership of ρH-p(B) is expressed by the L-p property of the functions. As an application, we can characterize the boundedness and the compactness of the composition operator C-φ, defined by C-φ f = f &CIRC; φ, from the Bloch space into the Hardy space H-p(B). [References: 42]