PreprintCC BY 4.0arXiv
Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case
Abstract
We allow the exponent α that defines the positive Bergman operator on the upper half-plane to differ from the exponent γ that defines the underlying weighted Lebesgue spaces. In this setting, we prove a sharp weak-type off-diagonal weighted inequality, with explicit and best-possible dependence on the Békollé--Bonami characteristic of the weight. We then deduce strong-type off-diagonal inequalities for the same operator. The key new tool is an off-diagonal extrapolation theorem, adapted to allow a change in the power of the distance to the boundary along the way.
Related
- Norm of the generalized Hilbert operator on weighted Bergman spaces
- Parameter Dependence of Weighted Bergman Kernels Beyond Smoothness
- The Differential Hilbert Operator Between Weighted Bergman Spaces
- Sharp weighted estimates for the multilinear maximal operator
- Weighted Lq-Lr estimates of a generalized Oseen evolution operator in exterior domains, with applications to the Navier-Stokes flow past a rigid body
BibTeX
@misc{sehba2026sharp,
title = {{Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case}},
author = {Benoit F. Sehba},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.01159},
eprint = {2608.01159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.01159},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case
AU - Benoit F. Sehba
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2608.01159
UR - https://arxiv.org/abs/2608.01159
AB - We allow the exponent α that defines the positive Bergman operator on the upper half-plane to differ from the exponent γ that defines the underlying weighted Lebesgue spaces. In this setting, we prove a sharp weak-type off-diagonal weighted inequality, with explicit and best-possible dependence on the Békollé--Bonami characteristic of the weight. We then deduce strong-type off-diagonal inequalities for the same operator. The key new tool is an off-diagonal extrapolation theorem, adapted to allow a change in the power of the distance to the boundary along the way.
ER -