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arXiv · 2608.22811

The Douglas question for functions of the form $\bar{z}+h$ with $h$ in the disk algebra

Jiawei Wang·Xianfeng Zhao
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Abstract

We prove that the Toeplitz operator $T_{\bar{z}+h}$ is invertible on the Bergman space provided that $|\bar{z}+h|$ is bounded below by some positive constant on the open unit disk, where $h$ is in the disk algebra. This provides a general class of harmonic functions for which the answer to the Douglas question on the Bergman space is affirmative.

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Jiawei Wang, Xianfeng Zhao. 2026-08-24. The Douglas question for functions of the form $\bar{z}+h$ with $h$ in the disk algebra. https://arxiv.org/abs/2608.22811

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