Koppelman formulas on the A1-singularity

2014/07/31 by Richard Lärkäng, Jean Ruppenthal · 6 citations
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Bar (unit) #Homotopy and Cohomology in Algebraic Topology #Mathematical analysis #Mathematics #Operator (biology) #Physics #Pure mathematics #Singularity #math.CV

paper · pdf · doi:10.1016/j.jmaa.2015.12.028

published in Journal of Mathematical Analysis and Applications 437(1), 214-240 (Elsevier BV) · 23 pages. v3: Minor changes made for the final version

openalex publication_date 2015/12/22 · arxiv created 2017/05/29 · arxiv updated 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In the present paper, we study the regularity of the Andersson-Samuelsson Koppelman integral operator on the A₁-singularity. Particularly, we prove L^p- and C⁰-estimates. As applications, we obtain L^p-homotopy formulas for the ∂-equation on the A₁-singularity, and we prove that the A-forms introduced by Andersson-Samuelsson are continuous on the A₁-singularity.

Citations

• Holomorphic Functions and Integral Representations in Several Complex Variables
• Koppelman formulas on affine cones over smooth projective complete intersections

Cited by

• Koppelman formulas on affine cones over smooth projective complete intersections