AI 中文总结
该研究针对Hardy-Littlewood极大算子、Calderón-Zygmund算子及其交换子，推导了对应算子$S_v$的双权弱型估计，拓展了权不等式相关研究成果。
AI 中文摘要
我们研究算子$S_v f = \boldsymbol{\textit{T}}(fv)/v$的双权弱型估计，其中$\boldsymbol{\textit{T}}$为Hardy-Littlewood极大算子或Calderón-Zygmund算子（CZO），$v$为权。具体而言，在涉及的权满足一定条件时，我们证明$S_v$是从$L^{1}(wv)$到$L^{1,\fty} (uv)$的有界算子。我们还考虑了当$\boldsymbol{\textit{T}}$为CZO的高阶交换子时对应的不等式，这类结果受文献[21]中Sawyer的文章启发（另见文献[17]）。
英文摘要
We study two-weight weak-type estimates for the operator $S_v f = \mathcal{T}(fv)/v$, where $\mathcal{T}$ is the Hardy-Littlewood maximal operator or a Calderón-Zygmund operator (CZO) and $v$ is a weight. Concretely, under certain conditions on the weights involved, we prove that $S_v$ is bounded from $L^{1}(wv)$ to $L^{1,\infty} (uv)$. We also consider the corresponding inequalities when $\mathcal{T}$ is a higher-order commutator of a CZO. These types of results are inspired by the article of Sawyer in [21], (see also [17]).
Comments23 pages
