Counterexample of an unbounded domain for ohsawa's problem

Abstract

In the Summer Seminar at Tateyama in Japan of Several Complex Variables, 18th July 1994, Professor T. Ohsawa posed the following problem in his talk [11].

PROBLEM (Ohsawa) Let Ω be a bounded pseudoconvex domain in C ⁿ and H be a one-codimensional complex linear subspace of C ⁿ. For any bounded holomorphic function g on Ω∩H, does there exist a bounded holomorphic function f on Ω such that the restriction f|Ω∩H of f to Ω∩H coincides with g on Ω∩H?

We give a counterexample for Ohsawa's Problem on bounded holomorphic extensions from hyperplanes to unbounded pseudoconvex domains.

AMS No.:

• 32J10
• 32F15