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\(L^p\) regularity of Toeplitz operators on generalized Hartogs triangles

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Abstract

We obtain \(L^p\) estimates for Toeplitz operators on the generalized Hartogs triangles \(\mathbb {H}_\gamma = \{(z_1,z_2) \in \mathbb {C}^2\,{:}\, |z_1|^\gamma \!< |z_2|<1\}\) for two classes of positive radial symbols, one a power of the distance to the origin, and the other a power of the distance to the boundary.

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Acknowledgements

We would like to thank the anonymous referees for constructive feedback.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, Los Angeles, CA, 90095, USA

    Meijke Balay

  2. School of Mathematics, University of Minnesota, Twin Cities, Minneapolis, MN, 55455, USA

    Trent Neutgens

  3. Department of Mathematics, Carleton College, Northfield, MN, 55057, USA

    Nick Rosen

  4. Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, MO, 63130, USA

    Nathan Wagner

  5. Department of Mathematics and Statistics, University of Michigan-Dearborn, Dearborn, MI, 48128, USA

    Yunus E. Zeytuncu

Authors
  1. Meijke Balay
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  2. Trent Neutgens
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  3. Nick Rosen
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  4. Nathan Wagner
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  5. Yunus E. Zeytuncu
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Correspondence to Yunus E. Zeytuncu.

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This project was completed as a part of the Polymath REU 2020; the authors thank the organizers and the participants of the program. This research was partially sponsored by NSF Grant DMS-1659203, NSF Grant DGE-1745038, and a Grant from the NSA.

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Balay, M., Neutgens, T., Rosen, N. et al. \(L^p\) regularity of Toeplitz operators on generalized Hartogs triangles. European Journal of Mathematics 8, 403–416 (2022). https://doi.org/10.1007/s40879-021-00505-5

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  • DOI: https://doi.org/10.1007/s40879-021-00505-5

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