Geodesic
Isometries of H p(U n)
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 92-95

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Forelli in [1] has described the isometries of Hp(U) into Hp(U) for p≠2, 0 < p < ∞. We shall extend his methods to characterize the isometries of Hp(Un) onto Hp(Un).The notation we shall use can be found in Rudin [3].Let II represent a permutation that induces a map on functions of n complex variables by Clearly II is an isometry of Hp(Un) onto Hp(Un). 
Schneider, R. B. Isometries of H p(U n). Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 92-95. doi: 10.4153/CJM-1973-007-0
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[1] 1. Frank, Forelli, The isometries of Hpt Can. J. Math. 16 (1964), 721–728. Google Scholar

[2] 2. Robert, Gunning and Hugo, Rossi, Analytic functions of several complex variables (Prentice Hall, New York, 1965). Google Scholar

[3] 3. Walter, Rudin, Function theory on polydiscs (Benjamin, New York, 1969). Google Scholar

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