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Difference of composition operators over the half-plane

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Abstract

To overcome the unboundedness of the half-plane, we use Khinchine’s inequality and atom decomposition techniques to provide joint Carleson measure characterizations when the difference of composition operators is bounded or compact from standard weighted Bergman spaces to Lebesgue spaces over the half-plane for all index choices. For applications, we obtain direct analytic characterizations of the bounded and compact differences of composition operators on such spaces. This paper concludes with a joint Carleson measure characterization when the difference of composition operators is Hilbert-Schmidt.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11771340 and 11431011). The authors thank the anonymous reviewers for their meaningful advice which improves the final version.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Changbao Pang & Maofa Wang

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  1. Changbao Pang
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  2. Maofa Wang
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Correspondence to Maofa Wang.

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Pang, C., Wang, M. Difference of composition operators over the half-plane. Sci. China Math. 63, 2299–2320 (2020). https://doi.org/10.1007/s11425-018-9439-2

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  • DOI: https://doi.org/10.1007/s11425-018-9439-2

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