Abstract. It is a fundamental problem in several complex variables to find solutions to the inhomogeneous Cauchy-Riemann equations that satisfy some kind of estimates. Using tools from complex analysis in one variable, one can write an explicit integral operator that solves the inhomogeneous Cauchy-Riemann equations on domains that are products of one-dimensional domains. I will show that such a solution satisfies supnorm estimates. I will also discuss weak solutions and a possible approach to an old question of Kerzman which is still open. The talk is based on joint work with Yifei Pan.
Supnorm estimates for the Cauchy-Riemann equations on product domains
29.10.2020 09:00 - 10:30
Organiser:
Bernhard Lamel
Location:
Zoom