发表机构
Delft University of Technology（代尔夫特理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在两类非倍测度背景下证明稀疏算子的混合$A_p$-$A_\infty$估计，获得与经典情形相同幂次的强、弱型界，并解决Rubio de Francia平方函数及Haar平移的开放问题。
AI 中文摘要
我们在两个非倍测度背景下证明了稀疏算子的混合$A_p$-$A_\infty$估计。在第一个背景下，我们考虑使用连续时间中的停时定义的稀疏算子。我们获得了与经典背景下相同幂次的权重特征的强型和弱型界。我们的一些弱型界即使对于$\mathbb R^d$上的二进滤过也是新的，并且特别地，蕴含了Rubio de Francia平方函数的尖锐弱型$(2,2)$估计，解决了Garg、Roncal和Shrivastava [J. Geom. Anal., 31:748-771, 2021]留下的一个开放问题。在第二个背景下，我们考虑二进稀疏形式，其中不同的立方体可以相互作用，只要它们的二进距离有界。我们获得了与经典背景下相同幂次的权重特征的强型界。作为一维应用，我们获得了平衡非倍测度上Haar平移的强型界，回答了Conde-Alonso、Pipher和Wagner [Math. Ann., 391:2209-2253, 2025]提出的一个定量问题。
英文摘要
We prove mixed $A_p$-$A_\infty$ estimates for sparse operators in two non-doubling settings. In the first setting, we consider sparse operators defined using stopping times in continuous time. We obtain both strong- and weak-type bounds with the same powers of the weight characteristics as in the classical setting. Some of our weak-type bounds are even new for the dyadic filtration on $\mathbb R^d$ and, in particular, imply a sharp weak-type $(2,2)$ estimate for Rubio de Francia square functions, solving a problem left open by Garg, Roncal and Shrivastava [J. Geom. Anal., 31:748-771, 2021]. In the second setting, we consider dyadic sparse forms in which distinct cubes may interact, provided their dyadic distance is bounded. We obtain strong-type bounds with the same powers of the weight characteristics as in the classical setting. As a one-dimensional application, we obtain strong-type bounds for Haar shifts over balanced non-doubling measures, answering a quantitative question posed by Conde-Alonso, Pipher, and Wagner [Math. Ann., 391:2209-2253, 2025].
Comments35 pages
