Speaker：Jin Tao（Hubei University）

Time：2023-3-6, 10:00

Location：Tencent Meeting ID：339-984-122（No Password）

Abstract:

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.