The group of isometries on Hardy spaces of the n-ball and the polydisc

Abstract

Let C be the complex plane, and U the disc |z| < 1 in C. Cn denotes complex n-dimensional Euclidean space, <, > the inner product, and | · | the Euclidean norm in Cn. Bn will be the open unit ball {z ∈ Cn: |z| < 1}, and Un will be the unit polydisc in Cn. For 1 ≤p<∞, p≠2, Gp(Bn) (resp., Gp (Un)) will denote the group of all isometries of Hp (Bn) (resp., Hp (Un)) onto itself, where Hp (Bn) and Hp (Un) are the usual Hardy spaces.