Koppelman formulas on the A_1-singularity

Journal article, 2016

In the present paper, we study the regularity of the Andersson-Samuelsson Koppelman integral operator on the A_1-singularity. Particularly, we prove L^p- and C^0-estimates. As applications, we obtain L^p-homotopy formulas for the dbar-equation on the A_1-singularity, and we prove that the A-forms introduced by Andersson-Samuelsson are continuous on the A_1-singularity.