Products of redial derivative and integral-type operators from Zygmund spaces to Bloch spaces

Ning Xu

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arXiv · 1111.5126

Products of redial derivative and integral-type operators from Zygmund spaces to Bloch spaces

Ning Xu

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Abstract

Let $H(\mathbb{B})$ denote the space of all holomorphic functions on the unit ball $\mathbb{B}\in \mathbb{C}^n$. In this paper we investigate the boundedness and compactness of the products of radial derivative operator and the following integral-type operator $$ I_ϕ^g f(z)=\int_0^1 \Re f(ϕ(tz))g(tz)\frac{dt}{t},\ z\in\mathbb{B} $$ where $g\in H(\mathbb{B}), g(0)=0$, $ϕ$ is a holomorphic self-map of $\mathbb{B}$,\ between Zygmund spaces and Bloch spaces.

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Ning Xu. 2011-11-22. Products of redial derivative and integral-type operators from Zygmund spaces to Bloch spaces. https://arxiv.org/abs/1111.5126

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