Domains with Finite Dimensional Bergman Space.
Doubly commuting submodules of the Hardy module over polydiscs
In this note we establish a vector-valued version of Beurling’s theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the “weak” completion problem in .
Duality theorems for Hardy and Bergman spaces on convex domains of finite type in
We study Hardy, Bergman, Bloch, and BMO spaces on convex domains of finite type in -dimensional complex space. Duals of these spaces are computed. The essential features of complex domains of finite type, that make these theorems possible, are isolated.
Editorial statement on the paper: The Corona theorem for the ball and polydisc.
Embedding derivatives of -harmonic tent spaces into Lebesgue spaces.
Ensemble des zéros d'une fonction holomorphe bornée dans la boule unité.
Ensembles suffisants pour quelques espaces de fonctions
Équations de Cauchy-Riemann tangentielles associées à un domaine de Siegel
Estimates for Derivates of Holomorphic Functions in Pseudoconvex Domains.
Extension and restriction of holomorphic functions
Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds of pseudoconvex domains to all of even in quite simple situations; The spaces are, in general, not at all preserved. Also the image of the Hilbert space under the restriction to can have a very strange structure.
Extension dans des classes de Hardy de fonctions holomorphes et estimations de type «mesures de Carleson» pour l’équation
Nous montrons qu’une fonction holomorphe sur un sous-ensemble analytique transverse d’un domaine borné strictement pseudoconvexe de admet une extension dans si et seulement si elle vérifie une condition de type à poids sur ; la démonstration est en partie basée sur la résolution de l’équation avec estimations de type “mesures de Carleson”.
Fatou and Korányi-Vági type theorems on the minimal ball.
In this paper we develop the Hp(p ≥ 1) theory on the minimal ball. After identifying the admissible approach regions, we establish theorems of Fatou and Koráanyi-Vági type on this ball.
Finite rank commutators of Toeplitz operators on the bidisk
We study some algebraic properties of commutators of Toeplitz operators on the Hardy space of the bidisk. First, for two symbols where one is arbitrary and the other is (co-)analytic with respect to one fixed variable, we show that there is no nontrivial finite rank commutator. Also, for two symbols with separated variables, we prove that there is no nontrivial finite rank commutator or compact commutator in certain cases.
Fonctions holomorphes bornées sur la boule unité de Cn.
Fonctions intérieures dans la boule unité de ...n dont les fonctions traces sont aussi intérieures.
Formulars for the L...-minimal solutions of the ...-equation in the unit ball of C...
Fredholm Toeplitz operators on strongly pseudoconvex domains
Generalized Hardy spaces on tube domains over cones
We define a class of spaces , 0 < p < ∞, of holomorphic functions on the tube, with a norm of Hardy type: . We allow μ to be any quasi-invariant measure with respect to a group acting simply transitively on the cone. We show the existence of boundary limits for functions in , and when p ≥ 1, characterize the boundary values as the functions in satisfying the tangential CR equations. A careful description of the measures μ when their supports lie on the boundary of the cone is also provided....
Growth of functions in tubes.
spaces in tubes and distributional boundary values