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

2026/08/02 by Benoit F. Sehba
Mathematics · #math.CA #math.CV #math.FA

paper · pdf

8 pages

arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

We prove sharp weak and strong off-diagonal weighted inequalities for the positive Bergman operator on the upper half-plane when the parameter defining the operator is not necessarily the same as the one of the weighted Lebesgue spaces in consideration. The inequalities are obtained with the help of an adapted off-diagonal extrapolation result.

Citations

• Weighted norm inequalities for fractional Bergman operators
• Sharp Bekolle estimates for the Bergman projection
• A simple proof of the A₂ conjecture
• The sharp weighted bound for general Calderon-Zygmund operators
• Sharp constants related to the triangle inequality in Lorentz spaces
• Heating of the Ahlfors-Beurling operator: weakly quasiregular maps on the plane are quasiregular