Bergman–Toeplitz operators on fat Hartogs triangles

Khanh, Tran Vu; Liu, Jiakun; Thuc, Phung Trong

doi:10.1090/proc/14218

Bergman–Toeplitz operators on fat Hartogs triangles
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by Tran Vu Khanh, Jiakun Liu and Phung Trong Thuc

Proc. Amer. Math. Soc. 147 (2019), 327-338

DOI: https://doi.org/10.1090/proc/14218

Published electronically: October 3, 2018

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Abstract:

In this paper, we obtain some $L^{p}$ mapping properties of the Berg- man–Toeplitz operator \[ f\longrightarrow T_{K^{-\alpha }}\left (f\right ):=\intop _{\Omega }K_{\Omega }\left (\cdot ,w\right )K^{-\alpha }\left (w,w\right )f\left (w\right )dV(w) \] on fat Hartogs triangles $\Omega _{k}:=\left \{ \left (z_{1},z_{2}\right )\in \mathbb {C}^{2}:\left |z_{1}\right |^{k}<\left |z_{2}\right |<1\right \}$, where $\alpha \in \mathbb {R}$ and $k\in \mathbb Z^+$.

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