Speaker：Yanping Chen（University of Science and Technology Beijing）

Time：2020-10-18 15:00

Location：Tencent Meeting ID：808 156 314（Pwd: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.