# zbMATH — the first resource for mathematics

Integral representation formulas for Cartan domains. (Formules de représentation intégrale pour les domaines de Cartan.) (French) Zbl 0948.32025
Author’s abstract: For a bounded, symmetric and circled domain $$D$$ in $$\mathbb C^n$$, considered as the unit ball of some Jordan triple system $$V$$, we give Koppelman-Leray and Cauchy-Leray formulas. These formulas supply us integral operators for solving the equation $$\overline\partial u =f$$ when $$f$$ is a closed $$(0,q)$$ form with coefficients in $$C^0(\overline D)$$. These operators, constructed by the help of the generic norm of $$V$$, are invariant by some Lie subgroup in the group of biholomorphic transformations of $$D$$, and the solutions obtained satisfy an estimation of growth at the boundary.
Reviewer: M.Stoll (Columbia)
##### MSC:
 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) 32W05 $$\overline\partial$$ and $$\overline\partial$$-Neumann operators
##### Keywords:
$$\bar\partial$$-problem; bounded symmetric domains
Full Text: