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Composition operators on Dirichlet spaces and Bloch space

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Abstract

In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.

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Authors and Affiliations

  1. Institute of Mathematics, School of Science, Tianjin University of Technology and Education, Tianjin, 300222, P. R. China

    Yuan Cheng

  2. Department of Mathematics, University of Jammu, Jammu, 180 006, India

    Sanjay Kumar

  3. Department of Mathematics, Tianjin University, Tianjin, 300072, P. R. China

    Ze Hua Zhou

  4. Center for Applied Mathematics of Tianjin University, Tianjin, 300072, P. R. China

    Ze Hua Zhou

Authors
  1. Yuan Cheng
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  2. Sanjay Kumar
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  3. Ze Hua Zhou
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Corresponding author

Correspondence to Ze Hua Zhou.

Additional information

The first author is supported by National Natural Science Foundation of China (Grant No. 11226086) and Tianjin Advanced Education Development Fund (Grant No. 20111005); the second author is supported by NBHM (DAE) Post-Doctoral Fellowship (Grant No. 2/40(32)/2009-R&D-II/1337); the third author is supported by National Natural Science Foundation of China (Grant Nos. 11371276, 10971153)

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Cheng, Y., Kumar, S. & Zhou, Z.H. Composition operators on Dirichlet spaces and Bloch space. Acta. Math. Sin.-English Ser. 30, 1775–1784 (2014). https://doi.org/10.1007/s10114-014-3171-y

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  • DOI: https://doi.org/10.1007/s10114-014-3171-y

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