Abstract
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 HP(Dn, X) and not only to those from the “one-dimensional” classes HP(D, X).
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Literature cited
A. V. Bukhvalov, “Hardy spaces of vector-valued functions,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,65, 5–16 (1976).
A. V. Bukhvalov and A. A. Danilevich, “Boundary properties of analytic and harmonic functions with values in a Banach space,” Mat. Zametki,31, No. 2, 203–214 (1982).
W. Hensgen, Hardy-Räume vektorwertiger Funktionen. Dissertation, Universität München (1986).
W. Rudin, Function Theory in Polydiscs, Benjamin, New York (1969).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 178, pp. 163–165, 1989.
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Petrenko, K.B. Boundary properties of vector-valued analytic functions in a polydisc. J Math Sci 61, 2044–2045 (1992). https://doi.org/10.1007/BF01095668
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DOI: https://doi.org/10.1007/BF01095668