Hyperbolic Mean Growth of Bounded Holomorphic Functions in the Ball
نویسنده
چکیده
We consider the hyperbolic Hardy class %Hp(B), 0 < p < ∞. It consists of φ holomorphic in the unit complex ball B for which |φ| < 1 and sup 0<r<1 ∫ ∂B {%(φ(rζ), 0)} dσ(ζ) < ∞, where % 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 %Hp(B) is expressed by the Lp property of the functions. As an application, we can characterize the boundedness and the compactness of the composition operator Cφ, defined by Cφf = f ◦ φ, from the Bloch space into the Hardy space Hp(B).
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