Sparse Domination and Weighted Inequalities for the ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho $$\end{document}-Variation of Singular Integrals and Commutators

被引：0
作者：
Yongming Wen
Huoxiong Wu
Qingying Xue
机构：
[1] Minnan Normal University,School of Mathematics and Statistics
[2] Xiamen University,School of Mathematical Sciences
[3] Beijing Normal University,School of Mathematical Sciences
[4] Ministry of Education,Laboratory of Mathematics and Complex Systems
来源：
The Journal of Geometric Analysis | 2022年 / 32卷 / 12期
关键词：
Variation operators; Singular integrals; Commutators; Sparse operators; Quantitative weighted bounds; Hörmander conditions; 42B20; 42B25;
D O I：
10.1007/s12220-022-01059-y
中图分类号：
学科分类号：
摘要：
This paper gives pointwise sparse domination results for variation operators of singular integrals and commutators with kernels satisfying Lr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^r$$\end{document}-Hörmander conditions. As applications, we obtain strong-type quantitative weighted bounds for such variation operators, weak-type quantitative weighted bounds for the variation operators of singular integrals and quantitative weighted weak-type endpoint estimates for variation operators of commutators, which are completely new even in the un-weighted case. In addition, we also obtain local exponential decay estimates for such variation operators.
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