Counterexample of a bounded domain for ohsawa's problem

In the Summer Seminar at Tateyama in Japan on Several Complex variables, July l8, 1994, Professor T Ohsawa posed the following problem in his talk [13]. PROBLEM (Ohsawa) Let ω be a bounded pseudoconvex domain in Cn and H be a one-codimensional complex liner subspace of Cn . For any bounded holomorphic function g on ω⋓H, is there a bounded holomorphic function f on ω such that the restriction of f toω⋓H coincides with g on ω⋂H? The second author [17] gave a counterexample for the above problem in case that H is unbounded. In the present paper, we give a counterexample in case that ω is bounded, using N. Sibony's domain [16].