Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (5): 1467-1473.doi: 10.1016/S0252-9602(16)30082-0

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WANDERING SUBSPACES OF THE HARDY-SOBOLEV SPACES OVER Dn

Jiesheng XIAO1, Guangfu CAO2   

  1. 1. Nanhu College, Jiaxing University, Jiaxing 314001, China Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
    2. Department of Mathematics, South China Agricultural University, Guangzhou 510642, China
  • Received:2015-01-22 Revised:2016-03-23 Online:2016-10-25 Published:2016-10-25
  • Contact: Jiesheng XIAO,xiaojiesheng@126.com E-mail:xiaojiesheng@126.com
  • Supported by:

    This work was partially supported by the Natural Science Foundation of China (11271092, 11471143), the key research project of Nanhu College of Jiaxing University (N41472001-18).

Abstract:

In this paper, we show that for (log(2)/(3))/(2 log 2)≤β≤(1)/(2), 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 subset α={α1,…, αk} of {1,…,n}, WαS is a generating wandering subspace for Wα|S=(Mzα1|S,…, Mzαk|S), that is,[WαS]Wα|S=S, where WαS(S?zαiS).

Key words: wandering subspace, invariant subspace, Beurling's theorem, Hardy-Sobolev space, doubly commuting

CLC Number: 

  • 47A15
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