We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
Let U be an open convex subset of Cn, n belonging to N, such that the set of all polinomies is dense in the space of all holomorphic and complex functions on U, (H(U), t0), where t0 is the open-compact topology.We endow the space HK(U) of all holomorphic functions on U that have asymptotic expansion at the origin with a metric and we study a particular compact subset of HK(U).
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.
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.
The Gleason problem is solved on real analytic pseudoconvex domains in . In this case the weakly pseudoconvex points can be a two-dimensional subset of the boundary. To reduce the Gleason problem to a question it is shown that the set of Kohn-Nirenberg points is at most one-dimensional. In fact, except for a one-dimensional subset, the weakly pseudoconvex boundary points are -points as studied by Range and therefore allow local sup-norm estimates for .
We prove some finiteness theorems for differential nondegenerate meromorphic mappings of into ℙⁿ(ℂ) which share n+3 hyperplanes.