Generalizations of inequalities of Littlewood and Paley.
Generic subgroups of Aut
We prove that for a parabolic subgroup of the fixed points sets of all elements in are the same. This result, together with a deep study of the structure of subgroups of acting freely and properly discontinuously on , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold covered by and such that the group of deck transformations of the covering is “sufficiently generic”, then is isolated in .
Geometric regularity versus analytic regularity higher codimensional case
Geometric regularity versus functional regularity
Good-irreducible inner functions on a polydisc
An explicit formula is developed for Nevanlinna class functions whose behaviour at the boundary is “sufficiently rational” and is then used to deduce the uniqueness of the factorization of such inner functions. A generalization of a theorem of Frostman is given and the above results are then applied to the construction of good and/or irreducible inner functions on a polydisc.
spaces in tubes and distributional boundary values
Harmonic and analytic functions admitting a distribution boundary value
Hyperfunktionen und Sätze vom Typ Edge of the Wedge.
Inclusion operators in Bergman spaces on bounded symmetric domains in
Interpolation by Holomorphic Functions Smooth to the Boundary in the Unit Ball of Cn.
Interpolation Gevrey dans les domaines de type fini de
Interpolation Gevrey dans les domaines de type fini de C2.
...k + a-estimates of the ...-equation on the Hartogs triangle.
Levi flat hypersurfaces in with prescribed boundary : stability
Local geometry of zero sets of holomorphic functions near the torus.
Maps from the Two-Ball to the Three-Ball.
Maximum modulus sets
We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain of dimension . If is a smooth manifold of dimension and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in with the same smooth -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in vanishes or if is polynomially...
Maximum modulus sets and reflection sets
We study sets in the boundary of a domain in , on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to reflection sets, which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.
Mesures de Carleson d’ordre et solutions au bord de l’équation
Microlocal properties of ultradistributions. Composition and kernel type operators.