DOCUMENTA MATHEMATICA, Vol. 5 (2000), 1-13

Atallah Affane

Formules de Représentation Intégrale pour les Domaines de Cartan

For a bounded, symmetric and circled domain $D$ in $\mathbf{C}^{n},\;$% 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.

1991 Mathematics Subject Classification: 32M15, 32F20.

Keywords and Phrases: $\overline{\partial }$-problem, bounded symmetric domains.

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