Sobolev regularity of the $$\overline{\partial }$$ -equation on the Hartogs triangle

Abstract

The regularity of the \(\overline{\partial }\)-problem on the domain \(\{\left|{z_1}\right|\!<\!\left|{z_2}\right|\!<\!1\}\) in \(\mathbb C ^2\) is studied using \(L^2\)-methods. Estimates are obtained for the canonical solution in weighted \(L^2\)-Sobolev spaces with a weight that is singular at the point \((0,0)\). In particular, the singularity of the Bergman projection for the Hartogs triangle is contained at the singular point and it does not propagate.