AI 中文总结
该说明性笔记概述调和分析中稀疏控制的核心思想，建立Komori-Shirai型加权Morrey空间上稀疏算子有界性的模型结果，为推导相关算子的Morrey空间估计提供简洁框架。
AI 中文摘要
稀疏控制是现代调和分析的核心工具，为Calderón-Zygmund算子及交换子算子、粗糙奇异积分、平方函数等相关算子的加权不等式提供了统一方法。在这篇说明性笔记中，我们简要概述了$L^p$空间与加权$L^p$空间上稀疏界背后的主要思想，并讨论稀疏算子在Morrey空间及广义Morrey空间上的有界性结果。我们建立了关于Komori-Shirai型加权Morrey空间$L^{p,\kappa}(w)$（其中$w\in A_p$）上稀疏算子有界性的模型结果。这些界为通过稀疏控制推导Calderón-Zygmund算子及相关算子的Morrey空间估计提供了更简洁的框架。最后，我们对其拓展性及与其他Morrey空间场景的联系进行了评述。
英文摘要
Sparse domination is a central tool in modern harmonic analysis, offering a unified approach to weighted inequalities for Calderón--Zygmund operators and related operators such as commutator operators, rough singular integrals, square functions etc. In this expository note, we briefly survey the main ideas behind sparse bounds on $L^p$ and weighted $L^p$ spaces, and discuss boundedness results for sparse operators on Morrey and generalized Morrey spaces. We establish a model result on the boundedness of sparse operators on Komori--Shirai type weighted Morrey spaces $L^{p,κ}(w)$, $w\in A_p$. These bounds offer a simpler framework for deriving Morrey-space estimates for Calderón--Zygmund operators and related operators via sparse domination. We conclude with remarks about extensions and connections to other Morrey space settings.
CommentsAccepted to Contemporary Mathematics special volume
