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Wandering subspaces and quasi-wandering subspaces in the Hardy–Sobolev spaces

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Abstract

In this paper, we prove that for −1/2 ≤ β ≤ 0, suppose M is an invariant subspaces of the Hardy–Sobolev spaces H β 2(D) for T z β, then M ⊖ zM is a generating wandering subspace of M, that is, \(M = {\left[ {M \ominus zM} \right]_{T_z^\beta }}\). Moreover, any non-trivial invariant subspace M of H β 2(D) is also generated by the quasi-wandering subspace P M T z βM⊥, that is, \(M = {\left[ {{P_M}T_z^\beta {M^ \bot }} \right]_{T_z^\beta }}\).

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Acknowledgements

The authors wish to thank referees for their many helpful comments and suggestions that greatly improved the paper.

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Authors and Affiliations

  1. Nanhu College, Jiaxing University, Jiaxing, 314001, P. R. China

    Jie Sheng Xiao

  2. Department of Mathematics, South China Agricultural University, Guangzhou, 510642, P. R. China

    Guang Fu Cao

Authors
  1. Jie Sheng Xiao
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  2. Guang Fu Cao
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Correspondence to Guang Fu Cao.

Additional information

Supported by National Natural Science Foundation of China (Grant No. 11671152) and the key research project of Nanhu College of Jiaxing University (Grant No. N41472001–18)

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Xiao, J.S., Cao, G.F. Wandering subspaces and quasi-wandering subspaces in the Hardy–Sobolev spaces. Acta. Math. Sin.-English Ser. 33, 1684–1692 (2017). https://doi.org/10.1007/s10114-017-7041-2

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  • DOI: https://doi.org/10.1007/s10114-017-7041-2

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