Koppelman Formulas on Affine Cones Over Smooth Projective Complete Intersections
Journal article, 2018

In the present paper, we study regularity of the Andersson-Samuelsson Koppelman integral operator on affine cones over smooth projective complete intersections. Particularly, we prove L-p- and C-alpha-estimates, and compactness of the operator, when the degree is sufficiently small. As applications, we obtain homotopy formulas for different partial derivative-operators acting on L-p-spaces of forms, including the case p = 2 if the varieties have canonical singularities. We also prove that the A-forms introduced by Andersson-Samuelsson are C-alpha for alpha < 1.

Singular complex spaces

Cauchy-Riemann equations



Richard Lärkäng

Bergische Universität Wuppertal

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Jean Ruppenthal

Bergische Universität Wuppertal

Indiana University Mathematics Journal

0022-2518 (ISSN)

Vol. 67 2 753-780

Subject Categories

Algebra and Logic


Mathematical Analysis



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