speaker:Mingming Cao

time:  2025.12.11,10:00-11:00 am

 place: Tencent Meeting:123-504-723

 Abstract：

The celebrated T1 theorem due to David and Joum\'{e} gives a necessary and suffi dient condition for $L^2$ boundedness of singular integral operators $T$. This was extended by Villaroya in 2015 to obtain the compactness of $T$. However, the $T1$ theorem to deduce compactness of multilinear singutar integrals has been an open problem for almost ten years. In this talk we solve this long-standing problem. Our main approaches consist of the following new ingredients:(i) a resulting representation of a compact bilinear Calder\'{o}n-Zygmund operator as average of some compact bilinear dyadic shifts and paraproducts;(i) extrapolation of endpoint compactness for bilinear operators, and (ii) compacmess criterion in weighted Lorentz spaces.