报告人：陶金（湖北大学）

时  间：2023年3月6日上午10:00-11:30

地  点：腾讯会议ID：339-984-122（无密码）

内容摘要:

This talk consists of three parts.

In the first part, we show a $L^p$-to-$L^q$ compactness characterization of commutators generated by non-degenerate Calder\'on--Zygmund operators, where $1

In the second part, we show an equivalent characterization of the space XMO introduced by R. H. Torres and Q. Xue, which is defined to be the closure in $\mathrm{BMO}\,({\mathbb R}^n)$ of all infinitely differentiable functions whose all derivatives converge to $0$ when $|x|\to\infty$. As an application of this characterization, we completely answer a question posed by Torres and Xue on the nontriviality of XMO.

In the third part, we introduce two vanishing subspaces of the John--Nirenberg space $JN_p({\mathbb R}^n)$, denoted by $VJN_p({\mathbb R}^n)$ and $CJN_p({\mathbb R}^n)$. Also, we equivalently characterize them via the limit behaviors of mean oscillations.

Moreover, several related follow-up works and some open questions are also mentioned in this talk.

个人简介：

陶金，湖北大学助理教授，2022年博士毕业于北京师范大学。陶金博士的研究方向是调和分析和函数空间及其应用，主要从事John—Nirenberg型空间以及奇异积分交换子的紧性问题等相关问题的研究，相关成果发表于Math. Ann., J. Fourier Anal. Appl., Sci. China Math., Potential Anal.等国内外重要学术期刊上。

联系人：杨东勇