Extension of Proper Holomorphic Mappings Past the Boundary.
Fonction de Green pluricomplexe et mesures pluriharmoniques
Fonctions plurisousharmoniques d'exhaustion bornées et domaines taut.
Formulas for approximate solutions of the ∂∂`-equation in a strictly pseudoconvex domain.
Let D be a bounded strictly pseudoconvex domain in Cn. We construct approximative solution formulas for the equation i∂∂`u = θ, θ being an exact (1,1)-form in D. We show that our formulas give simple proofs of known estimates and indicate further applications.
Geometry of hypersurfaces and mapping theorems in Cn.
Global boundary regularity for the -equation on -pseudo-convex domains
For a bounded domain of , we introduce a notion of «-pseudoconvexity» of new type and prove that for a given -closed -form that is smooth up to the boundary on , and for , there exists a -form smooth up to the boundary on which is a solution of the equation
Global Real Analyticity of Solutions to the ...-Neumann Problem.
Global regularity of the ...-Neumann problem on an annulus between two pseudoconvex manifolds which satisfy property (p).
Global regularity of the ...-Neumann problem on circular domains.
Growth Properties of Pseudo-Convex Domains and Domains of Holomorphy in Locally Convex Topological Vector Spaces.
Henkin-Ramirez formulas with weight factors
We construct a generalization of the Henkin-Ramírez (or Cauchy-Leray) kernels for the -equation. The generalization consists in multiplication by a weight factor and addition of suitable lower order terms, and is found via a representation as an “oscillating integral”. As special cases we consider weights which behave like a power of the distance to the boundary, like exp- with convex, and weights of polynomial decrease in . We also briefly consider kernels with singularities on subvarieties...
Higher asymptotics of the complex Monge-Ampère equation
Hinfty + LE in several variables.
Hodge Spectral Sequence on Pseudoconvex Domains.
Hölder and LP Estimates for ...b on Weakly Pseudo-Convex Boundaries in C2.
Hölder continuity of proper holomorphic mappings
We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.
Hölder regularity for solutions to complex Monge-Ampère equations
We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is and the right hand side has a density in for some p > 1, and prove the Hölder continuity of the solution.
Hölder Type Estimates for the -equation in Strongly Pseudoconvex Domains
Hölderabschätzungen für Ableitungen von Lösungen der Gleichung ...= f bei streng pseudokonvem Rand.
Holomorphe Funktionen auf Gebieten über Banach-Räumen zu vorgegebenen Konvergenzradien.