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New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces \({L_{\vec{p}}(\mathbb{R}^d)}\)

Author

Listed:
  • Junjian Zhao

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China)

  • Wei-Shih Du

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan)

  • Yasong Chen

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China)

Abstract

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces L p → ( R d ) . We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of L p → ( R d ) . Our new results unify and refine the existing results in the literature.

Suggested Citation

  • Junjian Zhao & Wei-Shih Du & Yasong Chen, 2021. "New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces \({L_{\vec{p}}(\mathbb{R}^d)}\)," Mathematics, MDPI, vol. 9(3), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:227-:d:486300
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    References listed on IDEAS

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    1. A. G. Georgiadis & M. Nielsen, 2016. "Pseudodifferential operators on mixed-norm Besov and Triebel–Lizorkin spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 289(16), pages 2019-2036, November.
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