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Weighted Composition Operators From \(H^\infty \) into the Zygmund Spaces

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Abstract

In this work we characterize the bounded and the compact weighted composition operators from the space \(H^\infty \) of bounded analytic functions on the open unit disk into the Zygmund space and the little Zygmund space. We also provide boundedness and compactness criteria of the weighted composition operators from the Bloch space into the little Zygmund space. In particular, we show that the bounded operators between these spaces are necessarily compact.

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Acknowledgments

We wish to express our gratitude to the referee for his/her valuable comments for the improvement of the manuscript. The second author is supported by Guangdong Natural Science Foundation (No. 10451401501004305), Foundation for Distinguished Young Talents in Higher Education of Guangdong (No. LYM11117) and National Natural Science Foundation of China (No. 11001107).

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Authors and Affiliations

  1. Department of Mathematical Sciences, George Mason University, Fairfax, VA, 22030, USA

    Flavia Colonna

  2. Department of Mathematics, JiaYing University, 514015 , Meizhou, GuangDong, China

    Songxiao Li

Authors
  1. Flavia Colonna
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  2. Songxiao Li
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Correspondence to Flavia Colonna.

Additional information

Communicated by Scott McCullough.

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Colonna, F., Li, S. Weighted Composition Operators From \(H^\infty \) into the Zygmund Spaces. Complex Anal. Oper. Theory 7, 1495–1512 (2013). https://doi.org/10.1007/s11785-012-0260-8

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