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Integral-type operators from a mixed norm space to a bloch-type space on the unit ball

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Abstract

Let \( \mathbb{B} \) be the unit ball in ℂn and let H(\( \mathbb{B} \)) be the space of all holomorphic functions on \( \mathbb{B} \). We introduce the following integral-type operator on H(\( \mathbb{B} \)):

$$ I_\phi ^g (f)(z) = \int\limits_0^1 {\operatorname{Re} f(\phi (tz))g(tz)\frac{{dt}} {t}} ,z \in \mathbb{B}, $$

where g ε H(\( \mathbb{B} \)), g(0) = 0, and φ is a holomorphic self-map of \( \mathbb{B} \). Under study are the boundedness and compactness of the operator from the mixed norm space H(p, q, ϕ)(\( \mathbb{B} \)) to the Bloch-type space ℬ µ(\( \mathbb{B} \)).

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Authors and Affiliations

  1. Mathematical Institute of the Serbian Academy of Sciences, Belgrade, Serbia

    Stevo Stević

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  1. Stevo Stević
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Correspondence to Stevo Stević.

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Original Russian Text Copyright © 2009 Stević S.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1391–1400, November–December, 2009.

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Stević, S. Integral-type operators from a mixed norm space to a bloch-type space on the unit ball. Sib Math J 50, 1098–1105 (2009). https://doi.org/10.1007/s11202-009-0121-5

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