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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
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