PreprintarXiv licencearXiv
The Beurling-type theorem for powers of weighted Bergman shifts
Abstract
Let ℬα denote the shift operator on the weighted Bergman space A2α(𝔻). We prove that, for every integer k≥1, the Beurling-type theorem holds for ℬαk on A2α(𝔻) if and only if −1<α≤1. We also show that, for every α>−1, there exists a finite Blaschke product B such that MB admits a cyclic invariant subspace but fails the wandering subspace property.
Related
- The Critical Value for the Beurling-Type Theorem in Weighted Bergman Spaces
- 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
- Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case
- Localization and weighted theory on the Bergman spaces
BibTeX
@misc{xu2026beurlingtype,
title = {{The Beurling-type theorem for powers of weighted Bergman shifts}},
author = {Shibo Xu and Tao Yu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37035},
eprint = {2610.37035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37035},
}
RIS
TY - UNPB
TI - The Beurling-type theorem for powers of weighted Bergman shifts
AU - Shibo Xu
AU - Tao Yu
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.37035
UR - https://arxiv.org/abs/2610.37035
AB - Let ℬ_α denote the shift operator on the weighted Bergman space A^2_α(𝔻). We prove that, for every integer k≥1, the Beurling-type theorem holds for ℬ_α^k on A^2_α(𝔻) if and only if −1<α≤1. We also show that, for every α>−1, there exists a finite Blaschke product B such that M_B admits a cyclic invariant subspace but fails the wandering subspace property.
ER -