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Mathematische Zeitschrift

, Volume 291, Issue 1–2, pp 591–607 | Cite as

Bergman–Toeplitz operators on weakly pseudoconvex domains

  • Tran Vu KhanhEmail author
  • Jiakun Liu
  • Phung Trong Thuc
Article
  • 113 Downloads

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.

Keywords

Bergman kernel Berman projection Bergman–Toeplitz operator Schur’s test Pseudoconvex domain of finite type 

Mathematics Subject Classification

Primary 47B35 32T25 Secondary 32A25 32A36 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Mathematics and its Applications, School of Mathematics and Applied StatisticsUniversity of WollongongNSWAustralia

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