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Small Hankel operators on weighted Besov spaces
Abstract
We characterize bounded small Hankel operators from Bp(om) to Bq(om)̅ on the polydisc for 0<p,q<∞, under explicit conditions relating the kernel parameter to the weight. When q<p, boundedness is equivalent to a weighted Besov condition on the symbol; when p≤ q, it is equivalent to a weighted supremum condition on a shifted radial derivative. In particular, the diagonal case is characterized by the product Bloch space. The proof combines weighted Bergman duality and atomic factorization with local kernel estimates and randomized atomic tests.
Related
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BibTeX
@misc{li2026small,
title = {{Small Hankel operators on weighted Besov spaces}},
author = {Chen Li and Kai Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03901},
eprint = {2611.03901},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03901},
}
RIS
TY - UNPB
TI - Small Hankel operators on weighted Besov spaces
AU - Chen Li
AU - Kai Wang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03901
UR - https://arxiv.org/abs/2611.03901
AB - We characterize bounded small Hankel operators from B_p(om) to B_q(om)̅ on the polydisc for 0<p,q<∞, under explicit conditions relating the kernel parameter to the weight. When q<p, boundedness is equivalent to a weighted Besov condition on the symbol; when p≤ q, it is equivalent to a weighted supremum condition on a shifted radial derivative. In particular, the diagonal case is characterized by the product Bloch space. The proof combines weighted Bergman duality and atomic factorization with local kernel estimates and randomized atomic tests.
ER -