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arXiv · 2608.01159

Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case

Benoit F. Sehba
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Abstract

We settle the two-parameter sharp weighted theory for the positive Bergman operator on the upper half-plane: we allow the exponent $\alpha$ that defines the operator to differ from the exponent $\gamma$ that defines the underlying weighted Lebesgue spaces. In this setting, we prove sharp weak-type and strong-type off-diagonal weighted inequalities, with explicit and best-possible dependence on the B\'ekoll\'e--Bonami characteristic of the weight. 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.

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Benoit F. Sehba. 2026-08-02. Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case. https://arxiv.org/abs/2608.01159

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