The \(\overline \partial\)-problem for a form with distribution boundary value on a strictly pseudoconvex domain. (Résolution du \(\overline \partial\) pour les formes différentielles ayant une valeur au bord au sens des courants dans un domaine strictement pseudoconvexe.) (French. English summary) Zbl 1229.32014

Sambou, Salomon; Sané, Mansour

Ann. Math. Blaise Pascal 18, No. 2, 323-331 (2011).

Summary: We solve the \(\overline \partial\) equation for forms with distribution boundary values on strictly pseudoconvex domains in \(\mathbb C^{ n }\).

MSC:

32F10	\(q\)-convexity, \(q\)-concavity
32F32	Analytical consequences of geometric convexity (vanishing theorems, etc.)

Keywords:

Cauchy-Riemann equation; boundary value in the sense of distributions; extensible current

References:

[1]	C. Laurent-Thiebault, J. Leiterer, Andreotti-vesentini separation theorem with \(C^k\) estimates and extension of \(CR\) forms, Mathematical Notes, 38 Princeton University, 416-436, (1993) · Zbl 0776.32012
[2]	Chirka, E. M., Regularization and \(\bar{∂ }\)-homotopy on a complex manifold, Soviet Math. Dolk., 20, 73-76, (1979) · Zbl 0445.32007
[3]	Lojaciewiecz, S.; Tomassini, G.; Scuola. Norm. Sup. Pisa, Pisa, Several Complex Variables, Valeurs au bord des forms holomorphes, 222-246, (1978), Cortona, 1976 77 · Zbl 0445.58028
[4]	Martineau, A., Theory of Distributions (Proc. Internat. Summer Inst., Lisbon, 1964), Distributions et valeurs au bord des fonctions holomorphes, 193-326, (1964), Inst. Gulbenkian Ci., Lisbon
[5]	Sambou, S., Résolution du \(\bar{∂ }\) pour LES courants prolongeables, Math. Nachrichten, 235, 179-190, (2002) · Zbl 1007.32012