Sobolev estimates for the ?-Neumann operator on domains in Cn admitting a defining function that is plurisubharmonic on the boundary.
Sobolev space estimates for solutions of the equation on polycylinders.
Solution of the ?-Equation with Uniform Estimates on Strictly q-Convex Domains with Non-Smooth Boundary.
Solution operators for the ...-equation on non-transversal intersections.
Solutions de l’équation et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudo-convexes
Il est montré que la condition de Blaschke est nécessaire et suffisante pour qu’un sous-ensemble analytique du domaine soit l’ensemble des zéros d’une fonction de la classe de Nevanlinna.
Solutions to -equations on strongly pseudo-convex domains with -estimates.
Some applications of the trace condition for pluriharmonic functions in Cn.
In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.
Some open problems in higher dimensional complex analysis and complex dynamics.
We present a collection of problems in complex analysis and complex dynamics in several variables.
Spectral Asymptotics for the -Neumann Problem
Spectrum of certain Banach algebras and ∂̅-problems
We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.
Splitting of the ∂-complex in weighted spaces of square integrable functions.
Stein Neighborhoods for Finite Preimages of Regular Domain.
Sur une extension du problème de Gleason dans les domaines pseudoconvexes
Dans cet article on montre que toute a une décomposition avec pour les domaines pseudoconvexes à frontière réelle-analytique et aussi pour les domaines pseudoconvexes pour lesquels le résultat soit valable localement.
The cohomology solution and the index theorem on ring surfaces of genus .
The equation the intersection of pseudoconvex domains
Viene studiata l'equazione per le forme regolari sulla chiusura dell'intersezione di domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme .
The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman
We give a short proof of the extension theorem of Ohsawa-Takegoshi. The same method also gives a generalization of the -theorem of Donnelly and Fefferman for the case of -forms.
The globally homeomorphic solutions to Beltrami system in Cn.
The Kernel of the ...-Neumann Operator on Strictly Pseudoconvex Domains.
The -Cauchy problem on weakly -pseudoconvex domains in Stein manifolds
Let be a Stein manifold of complex dimension and be a relatively compact domain with smooth boundary in . Assume that is a weakly -pseudoconvex domain in . The purpose of this paper is to establish sufficient conditions for the closed range of on . Moreover, we study the -problem on . Specifically, we use the modified weight function method to study the weighted -problem with exact support in . Our method relies on the -estimates by Hörmander (1965) and by Kohn (1973).
The local boundary regularity of the solution of the -equation