报告题目：Near-Endpoints Carleson embedding of Qs and F(p, q, s) into tent spaces

报 告 人：周小静 (汕头大学)

报告时间：2024年7月12日(周五) 16:00-17:00

报告地点：龙洞校区教学楼103

主 持 人：刘军明

报告摘要：This talk aims to report some recent progress in the study of the Qs and F(p, q, s) Carleson embedding problems. We first show that for 0<t<s<1, mu is an s-Carleson measure if and only if id: Qt mapsto T_{s, 2}^2(mu) is bounded. Using the same idea, we also prove a near-endpoints Carleson embedding for F(p, p alpha-2, s) for alpha>1. Our method is different from the previously known approach which involves a delicate study of Carleson measures (or logarithmic Carleson measures) on weighted Dirichlet spaces. As some byproducts, the corresponding compactness results are also achieved. Finally, we compare our approach with the existing solutions of Carleson embedding problems proposed by Xiao, Pau, Zhao, Zhu, etc. Our results assert that a ``tiny-perturbed" version of a conjecture on the Qs Carleson embedding problem due to Liu, Lou, and Zhu is true. Moreover, we answer an open question by Pau and Zhao on the F(p, q, s) Carleson embedding near endpoints. This talk is based on a recent joint work with Bingyang Hu.

简介： 周小静，汕头大学博士生。研究方向是解析函数空间与算子理论。在Banach Journal of Mathematical Analysis，Complex Analysis and Operator Theory等国际期刊上发表了多篇高水平学术论文。曾获得2023年度汕头大学Alan McIntosh纪念奖学金。