Commutators for certain fractional type operators on weighted spaces and Orlicz–Morrey spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-28 DOI:10.1007/s43037-024-00325-1

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引用次数: 0

Abstract

In this paper, we focus on a class of fractional type integral operators that can be served as extensions of Riesz potential with kernels $$\begin{aligned} K(x,y)=\frac{\Omega _1(x-A_1 y)}{|x-A_1 y |^{{n}/{q_1}}} \cdots \frac{\Omega _m(x-A_m y)}{|x-A_m y |^{{n}/{q_m}}}, \end{aligned}$$ where $\alpha \in [0,n)$ , $ m\geqslant 1$ , $\sum \limits _{i=1}^m\frac{n}{q_i}=n-\alpha $ , $\{A_i\}^m_{i=1}$ are invertible matrixes, $\Omega _i$ is homogeneous of degree 0 on $\mathbb R^n$ and $\Omega _i\in L^{p_i}(S^{n-1})$ for some $p_i\in [1,\infty )$ . Under appropriate assumptions, we obtain the weighted $L^p(\mathbb R^n)-L^q(\mathbb R^n)$ estimates as well as weighted $H^p(\mathbb R^n)-L^q(\mathbb R^n)$ estimates of the commutators for such operators with BMO-type function when $\frac{1}{q}=\frac{1}{p}-\frac{\alpha }{n}$ . In addition, we acquire the boundedness of these operators and their commutators with a function in Campanato spaces on Orcliz–Morrey spaces as well as the compactness for such commutators in a special case: $m=1$ and $A=I$ .

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加权空间和奥利兹-莫雷空间上某些分数型算子的换元器

摘要本文主要研究一类分数型积分算子，这些算子可以作为核为 $$\begin{aligned} 的 Riesz 势的扩展。K(x,y)=\frac{Omega _1(x-A_1 y)}{|x-A_1 y |^{{n}/{q_1}}}\cdots \frac{Omega _m(x-A_m y)}{|x-A_m y |^{{n}/{q_m}}}, \end{aligned}$$ 其中 $\alpha \in [0,n)$)、(m/geqslant 1\) 、(\sum \limits _{i=1}^m\frac{n}{q_i}=n-\alpha \)、(\{A_i\}^m_{i=1}\)都是可逆矩阵、 \在(\mathbb R^n\)上，(\Omega _i\)是0度同质的，并且对于某个$p_i\in [1,\infty )$ ，(\Omega _i\in L^{p_i}(S^{n-1})\)是同质的。在适当的假设条件下、当 $\frac{1}{q}=\frac{1}{p}-\frac{alpha }{n}$ 时，我们可以得到具有 BMO 型函数的此类算子的换向器的加权 $L^p(\mathbb R^n)-L^q(\mathbb R^n)$ 估计值以及加权 $H^p(\mathbb R^n)-L^q(\mathbb R^n)$ 估计值。此外，我们还获得了这些算子的有界性以及它们与奥克利茨-莫雷空间上的坎帕纳托空间中的函数的换元，以及在特殊情况下这些换元的紧凑性： $m=1$ 和 (A=I\) .

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.