Bergman-Toeplitz operators on fat Hartogs triangles

Tran Vu Khanh; Jiakun Liu; Phung Trong Thuc

Bergman-Toeplitz operators on fat Hartogs triangles

Complex Variables 2018-02-27 v1 Analysis of PDEs

Authors: Tran Vu Khanh , Jiakun Liu , Phung Trong Thuc

Abstract

In this paper, we obtain some $L^{p}$ mapping properties of the Bergman-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 $k\in \mathbb Z^+$ .

Keywords

toeplitz operators bergman spaces operator theory and elliptic operators

Cite

@article{arxiv.1802.09174,
  title  = {Bergman-Toeplitz operators on fat Hartogs triangles},
  author = {Tran Vu Khanh and Jiakun Liu and Phung Trong Thuc},
  journal= {arXiv preprint arXiv:1802.09174},
  year   = {2018}
}