Wandering subspaces of the hardy-sobolev spaces over Dn*Dn*

In this paper, we show that for log232log2≤β≤12, suppose S   is an invariant subspace of the Hardy-Sobolev spaces Hβ2(Dn) for the n  -tuple of multiplication operators (Mz1,⋯,Mzn)(Mz1,⋯,Mzn). If (Mz1|S,⋯,Mzn|S)(Mz1|S,⋯,Mzn|S) is doubly commuting, then for any non-empty sub-set α = {α1, …,αk} of {1, …, n  }, wαS is a generating wandering subspace for Mα|S=(Mzα1|S,⋯,Mzαk|S)Mα|S=(Mzα1|S,⋯,Mzαk|S), that is, [wαS]Mα|S=S, Where wαS=∩i=1k(SΘzαiS).