WANDERING SUBSPACES OF THE HARDY-SOBOLEV SPACES OVER Dn

doi:10.1016/S0252-9602(16)30082-0

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. 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

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 H_β²(Dⁿ) for the n-tuple of multiplication operators (M_z₁,…, M_{z_n}). If (M_z₁|_S,…, M_{z_n}|_S) is doubly commuting, then for any non-empty subset α={α₁,…, α_k} of {1,…,n}, W_α^S is a generating wandering subspace for W_α|_S=(M_{z_α1}|_S,…, M_{z_{α_k}}|_S), that is,[W_α^S]W_α|S=S, where W_α^S(S?z_{α_i}S).

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

CLC Number:

47A15

Jiesheng XIAO, Guangfu CAO. WANDERING SUBSPACES OF THE HARDY-SOBOLEV SPACES OVER Dⁿ[J].Acta mathematica scientia,Series B, 2016, 36(5): 1467-1473.

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WANDERING SUBSPACES OF THE HARDY-SOBOLEV SPACES OVER Dⁿ

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