Soohyun Park: Bergman space with a specific exponential weight on the complex unit ball

Abstract:

In this talk, we present results on weighted Bergman spaces on the complex unit ball, focusing on kernel estimates and Carleson measure characterization. We derive pointwise estimates for the Bergman kernel with an exponential weight, using the metric induced by the complex Hessian of \(\psi\), where the weight function is \(e^{-\phi}\). This work is motivated by Christ's result on reproducing kernel estimates in terms of the distance induced by the Laplacian of \(\phi\). Additionally, we characterize the Carleson measure, which provides conditions for the boundedness of Toeplitz operators with \(L^2\) symbols. This presentation is based on joint works with Hong Rae Cho and Han-Wool Lee.