报告题目：Capacitary Inequalities for Besov spaces of Generalized Smoothness

报告人：刘丽光

邀请人：熊棋

报告时间：2026年9月30日9:00-10:00

报告地点： 腾讯会议：596-684-748

摘要：We consider the Besov space $\dot{\Lambda}_{p,\, q,\, w}^{s}(\mathbb R^n)$, defined for parameters $p,\ q\in (1,\infty)$, smooth index $s\in (0,\infty)$ and a weight $w$ that imposes an additional smooth structure.If $w\equiv 1$, then it recovers the classical Besov space. If $w(x)= \left(\log \frac{e}{|x|\wedge 1}\right)^b$, then it coincides to the so-called logarithimic Besov spaces. We establish a strong type capacitary inequality for the capacity $\mathrm{Cap}_{s}^{p,\, q,\, w}$ that is associated with $\dot{\Lambda}_{p,\, q,\, w}^{s}(\mathbb R^n)$. This result is proved for the full range $s\in(0,\infty)$ and it significantly completes the Besov capacity theory initiated by Adams and Xiao

[Math. Ann. 325 (2003), 695--709], which was limited to the classical case $w\equiv 1$ and to the restricted range $s\in (0, n/p)$ as well as non-integer $s+n/q\in(0, 2n)$.This work is jointed with D. Jin (Renmin University), S. Wu (Dalian Maritime University) and J. Xiao (Memorial University).

报告人介绍：刘丽光，中国人民大学91暗网 教授，博导，国家级青年人才。主要从事调和分析方向的研究。至今已在《Adv. Math》《Appl. Comput. Harmon. Anal.》《J. Math. Pures. Appl.》《Math. Ann.》《J. Funct. Anal.》《Calc. Var. Partial Differential Equations》《J. Differential Equations》等数学期刊发表论文60余篇，并在Springer出版社《Lecture Notes in Math.》系列丛书发表专著1本。