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

Junjian Zhao, Wei-Shih Du and Yasong Chen
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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

Mathematics, 2021, vol. 9, issue 3, 1-10

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.

Keywords: mixed-norm; shift-invariant space; stability theorem; convolution type inequality; Hölder type inequality; Minkowski type inequality (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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