正伯格曼算子的尖锐加权范数估计：双参数情形
Sharp weighted norm estimates for the positive Bergman operator: the two-parameter case
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中文总结 AI 辅助
该研究针对上半平面中正伯格曼算子，在算子参数与加权勒贝格空间参数不一致的双参数情形，借助适配非对角外推结果，证明了尖锐弱、强型非对角加权不等式。
中文摘要 AI 辅助
我们证明了上半平面中正伯格曼算子的尖锐弱型与强型非对角加权不等式，其中定义算子的参数未必与所考虑的加权勒贝格空间的参数一致。这些不等式借助适配的非对角外推结果得到。
英文摘要
We settle the two-parameter sharp weighted theory for the positive Bergman operator on the upper half-plane: we allow the exponent $α$ that defines the operator to differ from the exponent $γ$ 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 Békollé--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.
发表机构
- University of Ghana（加纳大学）
机构由 AI 辅助整理，请以论文原文为准。
