Invited by Prof. Sibei Yang and Prof. Jun Gen from School of Mathematics and Statistics, Prof. Yanping Chen from University of Science and Technology Beijing will give a lecture online.

Title：An extension of Calder\'{o}n-Zygmund type singular integral with non-smooth kernel

Time：2:30 p.m.,Oct.20th, 2021

Conference ID:399 741 386( Tencent Conference)

Abstract:This paper is concerned with the generalized singular integral operator with rough kernel and the approximation problem for the generalized surface quasi-geostrophic equation. For the generalized singular integral operator, we obtain uniform $L^p-L^q$ estimates with respect to a parameter $\beta$. From this one can recover the $L^p$-boundedness of the Calder\'{o}n-Zygmund operator with rough kernel by letting $\beta\to 0$. We applied this estimate to study the Cauchy problem of the generalized surface quasi-geostrophic (SQG) equation. Local well-posedness in the Besov space $B^{s}_{p,q}$ and some limit behaviour of the solutions are obtained. This improves the previous results by Yu-Zheng-Jiu in 2019.