Affane, Atallah

Formules de représentation intégrale pour les domaines de Cartan.

Doc. Math., J. DMV 5, 1-13 (2000)


Summary: 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.

Mathematics Subject Classification

32M15, 32F20


$\overline{\partial }$-problem, bounded symmetric domains