摘要
In this paper, we show that for log(2/3)/2log2≤ β ≤1/2, suppose S is an invariant subspace of the Hardy-Sobolev spaces H_β~2(D^n) for the n-tuple of multiplication operators(M_(z_1),...,M_(z_n)). If(M_(z_1)|S,..., M_(z_n)|S) is doubly commuting, then for any non-empty subset α = {α_1,..., α_k} of {1,..., n}, W_α~S is a generating wandering subspace for M_α|_S =(M_(z_(α_1))|_S,..., M_(z_(α_k))|_S), that is, [W_α~S]_(M_(α |S))= S, where W_α~S=■(S ■ z_(α_i)S).
In this paper, we show that for log(2/3)/2log2≤ β ≤1/2, suppose S is an invariant subspace of the Hardy-Sobolev spaces H_β~2(D^n) for the n-tuple of multiplication operators(M_(z_1),...,M_(z_n)). If(M_(z_1)|S,..., M_(z_n)|S) is doubly commuting, then for any non-empty subset α = {α_1,..., α_k} of {1,..., n}, W_α~S is a generating wandering subspace for M_α|_S =(M_(z_(α_1))|_S,..., M_(z_(α_k))|_S), that is, [W_α~S]_(M_(α |S))= S, where W_α~S=■(S ■ z_(α_i)S).
基金
supported by the Natural Science Foundation of China(11271092,11471143)
the key research project of Nanhu College of Jiaxing University(N41472001-18)
