$$L^p(\mathbb {R}^d)$$ Boundedness for a Class of Nonstandard Singular Integral Operators

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-05 DOI:10.1007/s00041-024-10104-z

Jiecheng Chen, Guoen Hu, Xiangxing Tao

引用次数: 0

Abstract

In this paper, let $\Omega $ be homogeneous of degree zero which has vanishing moment of order one, A be a function on $\mathbb {R}^d$ such that $\nabla A\in \textrm{BMO}(\mathbb {R}^d)$, we consider a class of nonstandard singular integral operators, $T_{\Omega ,\,A}$, with rough kernel being of the form $ \frac{\Omega (x-y)}{\vert x-y\vert ^{d+1}}\big (A(x)-A(y)-\nabla A(y)(x-y)\big ) $. This operator is closely related to the Calderón commutator. We prove that, under the Grafakos-Stefanov minimum size condition $GS_{\beta }(S^{d-1})$ with $2<\beta <\infty $ for $\Omega $, $T_{\Omega ,\,A}$ is bounded on $L^p(\mathbb {R}^d)$ for p with $1+1/(\beta -1)< p < \beta $.

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一类非标准奇异积分算子的 $$L^p(\mathbb {R}^d)$$ 有界性

在本文中，让 $\Omega $ 是零度同调，它有一阶消失矩，A 是 $\mathbb {R}^d$ 上的函数，使得 $\nabla A\in \textrm{BMO}(\mathbb {R}^d)$、我们考虑一类非标准奇异积分算子，T(T_{\Omega ,\,A}\)，其粗核的形式是（（frac{\Omega (x-y)}{\vert x-y\vert ^{d+1}}}\big (A(x)-A(y)-\nabla A(y)(x-y)\big )\).这个算子与卡尔德龙换向器密切相关。我们证明，在格拉法科斯-斯特凡诺夫最小尺寸条件下 $GS_{\beta }(S^{d-1})$ with $2<\beta <；\(1+1/(\beta -1)< p < \beta$.

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.