PreprintCC0arXiv
The Douglas question for functions of the form z̅+h with h in the disk algebra
Abstract
We prove that the Toeplitz operator Tz̅+h is invertible on the Bergman space provided that |z̅+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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BibTeX
@misc{wang2026douglas,
title = {{The Douglas question for functions of the form $\barz+h$ with $h$ in the disk algebra}},
author = {Jiawei Wang and Xianfeng Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.22811},
eprint = {2608.22811},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.22811},
note = {CC0},
}
RIS
TY - UNPB
TI - The Douglas question for functions of the form z̅+h with h in the disk algebra
AU - Jiawei Wang
AU - Xianfeng Zhao
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2608.22811
UR - https://arxiv.org/abs/2608.22811
AB - We prove that the Toeplitz operator T_z̅+h is invertible on the Bergman space provided that |z̅+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.
ER -