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arXiv · 1407.5703

Koppelman formulas on the A_1-singularity

Richard Lärkäng·Jean Ruppenthal
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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.

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Richard Lärkäng, Jean Ruppenthal. 2014-07-22. Koppelman formulas on the A_1-singularity. https://doi.org/10.1016/j.jmaa.2015.12.028

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