On a Li–Stević integral-type operator from Bloch-type spaces into logarithmic Bloch spaces

Abstract

Let ϕ be an analytic self-map of the unit disk 𝔻, H(𝔻) the space of analytic functions on 𝔻 and g∈H(𝔻). Recently Li and Stević defined the following operator

on H(𝔻). The boundedness and compactness of the operator from the Bloch-type spaces into the logarithmic Bloch spaces are investigated in this paper.

Keywords:

• Bloch-type space
• logarithmic Bloch space
• composition operator
• Li–Stević integral-type operator

AMS Subject Classification :

• 47B38
• 47B33
• 30D55
• 46E15

Acknowledgement

The first author thanks Professors Shaozong Yan and Xiaoman Chen for their encouragement and help while visiting Fudan University. The authors also thank the referee for her/his many corrections. This work was supported by the Natural Science Foundation of China (10471039) and the Grant of Higher Schools’ Natural Science Basic Research of Jiangsu Province of China (06KJD110175, 07KJB110115).