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In this paper, I study the group of analytic automorphisms of a bounded product domain in the space$C(S,C)$of continuous functions on a compact space$S$. I prove that its automorphism group is a Lie group and I am able to prove which are the bounded symmetric ones.

First we define the dyadic Hardy space$H$_{$X$}$(d)$for an arbitrary rearrangement invariant space$X$on [0, 1]. We remark that previously only a definition of$H$_{$X$}$(d)$for$X$with the upper Boyd index$q$_{$x$}<∞ was available. Then we get a natural description of the dual space of$H$_{$x$}, in the case$X$having the property 1<-$p$_{$X$}<-$q$_{$X$}<2, imporoving an earlier result [P1].

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