Geodesic
Boundary properties of vector-valued analytic functions in polydiscs
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 163-165

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It is announced that the analytic Radon–Nikodym property (cf. [1]) is responsible for the boundary behaviour of functions in the vector Hardy classes $H^p(\mathbb{D}^n,X)$ in polydiscs (and not only in the disc). 
@article{ZNSL_1989_178_a7,
     author = {K. B. Petrenko},
     title = {Boundary properties of vector-valued analytic functions in polydiscs},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {163--165},
     publisher = {mathdoc},
     volume = {178},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a7/}
}
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K. B. Petrenko. Boundary properties of vector-valued analytic functions in polydiscs. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 18, Tome 178 (1989), pp. 163-165. http://geodesic.mathdoc.fr/item/ZNSL_1989_178_a7/