Koppelman formulas on the A_1-singularity

Abstract

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 $\bar{\partial }$-equation on the $A_1$-singularity, and we prove that the $\mathcal{A}$-forms introduced by Andersson-Samuelsson are continuous on the $A_1$-singularity.

23 pages. v3: Minor changes made for the final version

References in corpus (2)

• Koppelman formulas on affine cones over smooth projective complete intersections
• About the d-bar-equation at isolated singularities with regular exceptional set

Cited by in corpus (3)

• Koppelman formulas on affine cones over smooth projective complete intersections
• Estimates for the $\bar{\partial }$-equation on canonical surfaces
• Global Koppelman formulas on (singular) projective varieties