q-variation of singular integrals

：Prof. Chen Yanping
：2020-10-18 15:00
：Tencent Meeting APP

Speaker：Prof. Chen Yanping

         北京科技大学

Title: q-variation of singular integrals

Time：15:00, 18 Oct., 2020 

Location：Tencent Meeting APP (online)

会议ID：808 156 314

会议密码：1018

Abstract:

In this talk, first, we verify the L2-boundedness for the jump functions and variations of Calderón-Zygmund singular integral operators with the underlying kernels cancellation condition, in addition to some proper size and smooth conditions. This result should be the first general criteria for the variational inequalities for kernels not necessarily of convolution type. The L2-boundedness assumption that we verified here is also the starting point of the related results on the (sharp) weighted norm inequalities appeared in many recent papers. Second, we study the quantitative weighted bounds for the q-variational singular integral operators with rough kernels. The main result is for the sharp truncated singular integrals itself. it is the best known quantitative result for this class of operators, since when q=∞, it coincides with the best known quantitative bounds by Di Pilino--Hytönen--Li or Lerner. In the course of establishing the above estimate, we obtain several quantitative weighted bounds which are of independent interest.

Speaker Introduction：

陈艳萍，北京科技大学数理学院副院长，教授，博士生导师，2007年毕业于北京师范大学，获博士学位。主要从事调和分析及其应用研究。2009年获全国优秀博士学位论文提名论文奖，2011年，入选教育部新世纪优秀人才支持计划。自2007年以来，在Anal.&PDE、Trans.Amer.Math.Soc.、J.Funct.Anal.、Rev.Mat.Iberoam.、J.Goem.Anal.、Canada.J.Math.、Potential Analysis、中国科学(英文版)等国内外知名的杂志上发表多篇论文。

 

联系人：杨东勇