报告题目：Multiresolution analysis and Zygmund dilations

主 讲 人：李康伟

单位：天津大学

时间：9月21日9:00-10:00

腾讯ID：466-148-303

密码：230921

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 provide novel examples of Zygmund $A_p$ weights and Zygmund kernels showcasing the optimality of our kernel assumptions for weighted estimates.

简介：李康伟，国家"优秀青年科学基金"获得者，从事调和分析方向的研究工作，已在Adv. Math., Math. Ann.，J. Math. Pures. Appl.、IMRN, Trans. AMS及J. Funct. Anal.等国际知名期刊发表多篇论文。