Koppelman formulas on the A1-singularity

In the present paper, we study the regularity of the Andersson–Samuelsson Koppelman integral operator on the A1A1-singularity. Particularly, we prove LpLp- and C0C0-estimates. As applications, we obtain LpLp-homotopy formulas for the ∂¯-equation on the A1A1-singularity, and we prove that the AA-forms introduced by Andersson–Samuelsson are continuous on the A1A1-singularity.