PreprintarXiv licencearXiv
Localization and weighted theory on the Bergman spaces
Abstract
In this paper, we introduce the class of weakly localized operators on the weighted Bergman spaces induced by two-sided doubling weights. We first establish the characterization of the compactness of the operator belonging to the norm closure of weakly localized operators in terms of the boundary vanishing of the Berezin transform. Our approach here is different from the methods in the literature since the ``translation" operators are not served us a direct applicable tool in our setting. We further characterize the compactness of Toeplitz operators with bounded symbols in the two-weight setting, a boundedness criterion of a two-weight Bergman projection is also presented.
Related
- Norm of the generalized Hilbert operator on weighted Bergman spaces
- Compact linear combination of composition operators on weighted Bergman-Orlicz spaces induced by doubling weights
- The Critical Value for the Beurling-Type Theorem in Weighted Bergman Spaces
- Characterizations for quasiconformal weighted Bergman spaces
- Quantum harmonic analysis and the Differential operators on weighted Bergman spaces of bounded symmetric domains
BibTeX
@misc{duan2026localization,
title = {{Localization and weighted theory on the Bergman spaces}},
author = {Yongjiang Duan and Junhan Hong and Siyu Wang and Zipeng Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27713},
eprint = {2609.27713},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27713},
}
RIS
TY - UNPB
TI - Localization and weighted theory on the Bergman spaces
AU - Yongjiang Duan
AU - Junhan Hong
AU - Siyu Wang
AU - Zipeng Wang
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27713
UR - https://arxiv.org/abs/2609.27713
AB - In this paper, we introduce the class of weakly localized operators on the weighted Bergman spaces induced by two-sided doubling weights. We first establish the characterization of the compactness of the operator belonging to the norm closure of weakly localized operators in terms of the boundary vanishing of the Berezin transform. Our approach here is different from the methods in the literature since the ``translation" operators are not served us a direct applicable tool in our setting. We further characterize the compactness of Toeplitz operators with bounded symbols in the two-weight setting, a boundedness criterion of a two-weight Bergman projection is also presented.
ER -