Wandering subspaces of the hardy-sobolev spaces over Dn*

作者：Jiesheng XIAO; Guangfu CAO

来源：ACTA MATHEMATICA SCIENTIA, 2016, 36(5): 1467-1473.

DOI：10.1016/S0252-9602(16)30082-0

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). If (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), that is, [wαS]Mα|S=S, Where wαS=∩i=1k(SΘzαiS).

• 单位
  中山大学