Abstract
Let Q c C be a bounded symmetric domain of tube type with Shilov boundary S. On S? there is a Cauchy integral mapping function on 3 to holomorphic functions on Q. By a classical device and also by Hua [51 one can thus define a Poisson kernel on 3 x Q and a Poisson integral which maps functions on ? to functions on Q. Now any holomorphic or antiholomorphic function on Q is the Poisson integral ?P(f) of a hyperfunction on 3_; however, it is not true in general that every harmonic function on Q can be realized as the Poisson integral of some functional on S. How can one characterize the functions on Q which are the Poisson integrals of functionals on _? We now consider the following problem.
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