Boundary properties of vector-valued analytic functions in a polydisc

The result of the note consists in the fact that the Radon—Nikodym property (see A. V. Bukhvalov, Zap. Nauchn. Sem. LOMI, Vol. 65, pp. 5–16, 1976) corresponds to the boundary behavior of functions from the vector-valued Hardy classes H^P(Dⁿ, X) and not only to those from the one-dimensional classes H^P(D, X).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 163–165, 1989.