Seminar| Institute of Mathematical Sciences
Time：Friday, July 16th, 2021, 14:00-15:00
Location：R408, IMS
Speaker: Xin Dong, University of Connecticut
Abstract:We use weighted L^2-methods to obtain sharp pointwise estimates for the canonical solution to the Cauchy-Riemann equation on smoothly bounded strictly convex domains and the Cartan classical domain domains when the datum is bounded in the Bergman metric. We provide examples to show our pointwise estimates are sharp. In particular, we show that on the Cartan classical domains of rank 2 the maximum blow up order is greater than -log dist(z), which was obtained for the unit ball case by Berndtsson. Additionally, we obtain uniform estimates for the canonical solutions on the polydiscs, strictly pseudoconvex domains and the Cartan classical domains under stronger conditions on the data. This talk is based on a joint work (to appear in Analysis & PDE) with Li and Treuer.