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MR1066444 (92m:30079) 30F20 (30D50 30D55 46J15)
Hayashi, Mikihiro; Nakai, Mitsuru; Segawa, Shigeo Bounded analytic functions on two sheeted discs. Trans. Amer. Math. Soc. 333 (1992), no. 2, 799–819.
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