PreprintCC BY-NC-SA 4.0arXiv
The Bergman projection with operator weights
Abstract
We characterize boundedness of the Bergman projection on operator-weighted Lp spaces over a separable Hilbert space, for 1<p<∞. Under the directional integrability conditions, the criterion is uniform boundedness of averages over Carleson squares in the unit disc. We obtain norm estimates independent of dimension. The proof uses a separated kernel expansion and a layer decomposition of the tent tree. No reverse Hölder assumption is needed. We also give a finer matrix estimate with a dimension-dependent constant. Boundedness is unchanged by compactly supported changes of the weight that preserve the integrability conditions.
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BibTeX
@misc{chunxu2026bergman,
title = {{The Bergman projection with operator weights}},
author = {Xu Chunxu and Dong Jianxiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28521},
eprint = {2609.28521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28521},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The Bergman projection with operator weights
AU - Xu Chunxu
AU - Dong Jianxiang
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.28521
UR - https://arxiv.org/abs/2609.28521
AB - We characterize boundedness of the Bergman projection on operator-weighted L^p spaces over a separable Hilbert space, for 1<p<∞. Under the directional integrability conditions, the criterion is uniform boundedness of averages over Carleson squares in the unit disc. We obtain norm estimates independent of dimension. The proof uses a separated kernel expansion and a layer decomposition of the tent tree. No reverse Hölder assumption is needed. We also give a finer matrix estimate with a dimension-dependent constant. Boundedness is unchanged by compactly supported changes of the weight that preserve the integrability conditions.
ER -