Regularity of the Bergman Projection in Weakly Pseudoconvex Domains.
Regularity of the Bergman Projection on Domains with Transverse Symmetries.
Remarks on restriction eigenfunctions in .
Remarks on the Bergman kernel function of a worm domain
We use a recent result of M. Christ to show that the Bergman kernel function of a worm domain cannot be -smoothly extended to the boundary.
Reproducing kernels and multiple interpolation by holomorphic functions
Reproducing kernels for holomorphic functions on some balls related to the Lie ball
We consider holomorphic functions and complex harmonic functions on some balls, including the complex Euclidean ball, the Lie ball and the dual Lie ball. After reviewing some results on Bergman kernels and harmonic Bergman kernels for these balls, we consider harmonic continuation of complex harmonic functions on these balls by using harmonic Bergman kernels. We also study Szegő kernels and harmonic Szegő kernels for these balls.
Reproducing properties and -estimates for Bergman projections in Siegel domains of type II
On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space .
Residue integral formulas and the Radon transform for differential forms on q-linearly concave domains.
Residues, currents, and their relation to ideals of holomorphic functions.
Résidus et dualité.
Singularité de séries de Dirichlet associées à des polynômes de plusieurs variables et applications en théorie analytique des nombres
Soit un polynôme. On appelle série de Dirichlet associée à la fonction : . Dans cet article nous étudions l’existence et les propriétés du prolongement méromorphe d’une telle série sous l’hypothèse qu’il existe tel que : i) quand et et ii) où . Cette hypothèse est probablement optimale et en tout cas contient strictement toutes les classes de polynômes déjà traitées antérieurement. Sous cette hypothèse nos principaux résultats sont : l’existence du prolongement méromorphe au plan...
Sobolev Estimates for the Lewy Operator on Weakly Pseudo-Convex Boundaries.
Sobolev estimates for the ?-Neumann operator on domains in Cn admitting a defining function that is plurisubharmonic on the boundary.
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 to a class of polynomially generalized Bers–Vekua equations using Clifford analysis
In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure...
Some applications of Cauchy-Fantappie forms to (local) problems on
Some applications of the Bergman kernel to geometrical theory of functions
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 new estimates for distances in analytic function spaces of several complex variables and double Bergman representation formula.