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On an integral-type operator from Privalov spaces to Bloch-type spaces

Xiangling Zhu — 2011

Annales Polonici Mathematici

Let H(B) denote the space of all holomorphic functions on the unit ball B of ℂⁿ. Let φ be a holomorphic self-map of B and g ∈ H(B) such that g(0) = 0. We study the integral-type operator C φ g f ( z ) = ∫ 0 1 ℜ f ( φ ( t z ) ) g ( t z ) d t / t , f ∈ H(B). The boundedness and compactness of C φ g from Privalov spaces to Bloch-type spaces and little Bloch-type spaces are studied

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