|Date||Oct 05, 2023|
|Dept.||University of California at Irvine, USA|
In this talk, I will give a short survey on the sup-norm estimates for solutions of the Cauchy-Riemann equations. In particular, I will present a joint work with Dong and Treuer for the Cauchy-Riemann equations on the classical bounded symmetric domains, I will also present my recent work on sup-norm estimates for the canonical solution of the Cauchy-Riemann equations on the product domains with C 1,α boundary, which solves a problem posed by Kerzman in 1971. I will also connect the sup-norm estimate for the Cauchy-Riemann operator to Corona problem in several complex variables and introduce my recent work on it.