The Gleason problem for , , .
For , the boundary of the unit ball in , let . If then we call the exceptional set for . In this note we give a tool for describing such sets. Moreover we prove that if is a and subset of the projective -dimensional space then there exists a holomorphic function in the unit ball so that .
We solve the Dirichlet problem for line integrals of holomorphic functions in the unit ball: For a function which is lower semi-continuous on we give necessary and sufficient conditions in order that there exists a holomorphic function such that
We solve the following Dirichlet problem on the bounded balanced domain with some additional properties: For and a positive lower semi-continuous function on with for , we construct a holomorphic function such that for , where .
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