报告人：李康伟（天津大学）

邀请人：黄山林

报告时间：2023年10月17日（星期二）14:00-16:00

报告地点：腾讯会议：393 642 440

报告题目：Multiresolution analysis and Zygmund dilations

报告摘要：Zygmund dilations are a group of dilations lying in between the standard product theory and the one-parameter setting -- in $\mathbb R^3 = \mathbb R \times \mathbb R \times \mathbb R$ they are the dilations $(x_1, x_2, x_3) \mapsto (\delta_1 x_1, \delta_2 x_2, \delta_1 \delta_2 x_3)$. The dyadic multiresolution analysis and the related dyadic-probabilistic methods have been very impactful in the modern product singular integral theory. However, multiresolution analysis has not been understood in the Zygmund dilation setting or in other modified product space settings. In this talk I will introduce how to develop this missing dyadic multiresolution analysis of Zygmund type, and justify its usefulness by bounding, on weighted spaces, a general class of singular integrals that are invariant under Zygmund dilations. We providenovel examples of Zygmund $A_p$ weights and Zygmund kernels showcasing the optimality of our kernel assumptions for weighted estimates.

报告人简介：李康伟，2015年于南开大学取得博士学位，之后在芬兰赫尔辛基大学和西班牙巴斯克数学中心做博士后，现为天津大学数学应用数学中心教授，主要研究方向为调和分析，成果发表于Adv. Math、JMPA、Math. Ann.、JFA、TAMS等国际权威期刊。