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Bergman–Toeplitz operators on weakly pseudoconvex domains

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Abstract

We prove that for certain classes of pseudoconvex domains of finite type, the Bergman–Toeplitz operator \(T_{\psi }\) with symbol \(\psi =K^{-\alpha }\) maps from \(L^{p}\) to \(L^{q}\) continuously with \(1< p\le q<\infty \) if and only if \(\alpha \ge \frac{1}{p}-\frac{1}{q}\), where K is the Bergman kernel on diagonal. This work generalises the results on strongly pseudoconvex domains by Čučković and McNeal, and Abate, Raissy and Saracco.

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Authors and Affiliations

  1. Institute for Mathematics and its Applications, School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia

    Tran Vu Khanh, Jiakun Liu & Phung Trong Thuc

Authors
  1. Tran Vu Khanh
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  2. Jiakun Liu
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  3. Phung Trong Thuc
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Correspondence to Tran Vu Khanh.

Additional information

Khanh was supported by ARC Grant DE160100173; Liu was supported by ARC Grant DP170100929; Thuc was supported by PhD scholarship in ARC Grant DE140101366.

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Khanh, T.V., Liu, J. & Thuc, P.T. Bergman–Toeplitz operators on weakly pseudoconvex domains. Math. Z. 291, 591–607 (2019). https://doi.org/10.1007/s00209-018-2096-z

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  • DOI: https://doi.org/10.1007/s00209-018-2096-z

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