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Bergman Projection on the Symmetrized Bidisk

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Abstract

We apply the Bekollé–Bonami estimate for the (positive) Bergman projection on the weighted \(L^p\) spaces on the unit disk. As the consequences, we obtain the boundedness of the Bergman projection on the weighted Sobolev space on the symmetrized bidisk. We also improve the boundedness result of the Bergman projection on the unweighted \(L^p\) space on the symmetrized bidisk in Chen et al. (J Funct Anal 279(2):108522, 2020).

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Acknowledgements

We thank Loredana Lanzani for encouraging us to clarify the \(L^p\) boundedness of the Bergman projection on the symmetrized polydisk. Supported by National Science Foundation Grant DMS-1412384, Simons Foundation Grant #429722 and CUSE Grant Program at Syracuse University.

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Authors and Affiliations

  1. Department of Mathematics, Texas A &M University, College Station, TX 77843, USA

    Liwei Chen

  2. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA

    Muzhi Jin & Yuan Yuan

Authors
  1. Liwei Chen
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  2. Muzhi Jin
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  3. Yuan Yuan
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Correspondence to Yuan Yuan.

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Final Remark

Right before this manuscript is accepted for publication, Zhenghui Huo and Brett D. Wick showed in a preprint (cf. arXiv:2303.10002) that the sufficient condition in Remark 1.5 is in fact the necessary condition as well for the Bergman projection to be \(L^p\) bounded on the symmetrized polydisc.

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Chen, L., Jin, M. & Yuan, Y. Bergman Projection on the Symmetrized Bidisk. J Geom Anal 33, 204 (2023). https://doi.org/10.1007/s12220-023-01263-4

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  • DOI: https://doi.org/10.1007/s12220-023-01263-4

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