, Volume 6, Issue 1, pp 121-137

Composition Followed by Differentiation Between H and Zygmund Spaces

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Let \({\varphi}\) be an analytic self-map of the unit disk \({\mathbb{D}}\) , \({H(\mathbb{D})}\) the space of analytic functions on \({\mathbb{D}}\) and \({g \in H(\mathbb{D})}\) . The boundedness and compactness of the operator \({DC_\varphi : H^\infty \rightarrow { \mathcal Z}}\) are investigated in this paper.

Communicated by Joseph Ball.
This work was completed with the support of the Natural Science Foundation of China (10471039) and the Grant of Higher Schools’ Natural Science Basic Research of Jiangsu Province of China (06KJD110175, 07KJB110115).