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

The regularity of the $overline{partial }$ -problem on the domain ${left|{z_1}right|! 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.