Endpoint weak-type bounds beyond Calderón-Zygmund theory

arXiv - MATH - Functional Analysis Pub Date : 2024-09-13 DOI:arxiv-2409.08921

Zoe Nieraeth, Cody B. Stockdale

引用次数: 0

Abstract

We prove weighted weak-type $(r,r)$ estimates for operators satisfying $(r,s)$ limited-range sparse domination of $\ell^q$-type. Our results contain improvements for operators satisfying limited-range and square function sparse domination. In the case of operators $T$ satisfying standard sparse form domination such as Calder\'on-Zygmund operators, we provide a new and simple proof of the sharp bound $$ \|T\|_{L^1_w(\mathbf{R}^d)\rightarrow L^{1,\infty}_w(\mathbf{R}^d)} \lesssim [w]_1(1+\log [w]_{\text{FW}}). $$

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超越卡尔德龙-齐格蒙理论的端点弱型边界

我们证明了满足$(r,s)$有限范围稀疏支配的$\ell^q$型算子的加权弱型$(r,r)$估计。我们的结果包含了对满足有限范围和平方函数稀疏支配的算子的改进。对于满足标准稀疏形式支配（如 Calder\'on-Zygmund 算子）的算子 $T$ ，我们提供了一个新的、简单的尖锐约束的证明 $$ \|T\|_{L^1_w(\mathbf{R}^d)\rightarrow L^{1,\infty}_w(\mathbf{R}^d)} \lesssim[w]_1(1+\log [w]_{text{FW}}).$$

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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arXiv - MATH - Functional Analysis

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