Vanishing John--Nirenberg Spaces and Commutators
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：陶金（湖北大学）
：2023-03-06 10:00
：腾讯会议ID：339-984-122（无密码）
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 $1<q<p<\infty$. This improves a recent result of T. P. Hyt\"onen from boundedness to compactness.
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
