On the theorem of Frobenius for complex vector fields
On the -equation in a Banach space
Opérateurs pseudo-différentiels définis en un point
We introduce the notion of pseudo-differential operators defined at a point and we establish a canonical one-to-one correspondence between such an operator and its symbol. We also prove the invertibility theorem for special type operators.
Optimal Lipschitz estimates for the equation on a class of convex domains
Optimal Lp estimates for the ...-equation on complex ellipsoids in Cn.
Parabolic exhaustions and analytic coverings.
Pointwise estimates for the weighted Bergman projection kernel in , using a weighted estimate for the equation
Weighted estimates are obtained for the canonical solution to the equation in , where is a pseudoconvex domain, and is a strictly plurisubharmonic function. These estimates are then used to prove pointwise estimates for the Bergman projection kernel in . The weight is used to obtain a factor in the estimate of the kernel, where is the distance function in the Kähler metric given by the metric form .
...-problem on weakly q-convex domains.
Proper Maps from Strongly q-Convex Domains.
Radially symmetric plurisubharmonic functions
In this note we consider radially symmetric plurisubharmonic functions and the complex Monge-Ampère operator. We prove among other things a complete characterization of unitary invariant measures for which there exists a solution of the complex Monge-Ampère equation in the set of radially symmetric plurisubharmonic functions. Furthermore, we prove in contrast to the general case that the complex Monge-Ampère operator is continuous on the set of radially symmetric plurisubharmonic functions. Finally...
Randregularität des ...-Problems für die Halbkugel in ... .
Randregularität des ...-Problems für stückweise streng pseudokonvexe Gebiete in Cn.
Real anlytic regularity of the Bergman and Szegö projections on decoupled domains.
Régularité Gevrey au sens de Beurling ou Roumieu pour l'opérateur ... dans des ouverts non bornés.
Régularité hölderienne du ...b dans les hypersurfaces 1-convexes-concaves.
Regularity and Uniqueness of Solutions to Boundary Blow-up Problems for the Complex Monge-Ampère Operator
We prove that plurisubharmonic solutions to certain boundary blow-up problems for the complex Monge-Ampère operator are Lipschitz continuous. We also prove that in certain cases these solutions are unique.
Regularity of the Bergman Projection on Domains with Partial Transverse Symmetries.
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.
Remarks on the proof of a generalized Hartogs Lemma
This paper is an outgrowth of a paper by the first author on a generalized Hartogs Lemma. We complete the discussion of the nonlinear ∂̅ problem ∂f/∂z̅ = ψ(z,f(z)). We also simplify the proofs by a different choice of Banach spaces of functions.
Residue integral formulas and the Radon transform for differential forms on q-linearly concave domains.