Lebesgue and Hardy Spaces for Symmetric Norms II: A Vector-Valued Beurling Theorem

2014/08/05 by Yanni Chen, Chen, Yanni, Don Hadwin +3
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1408.1117

openalex publication_date 2014/08/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Suppose α is a rotationally symmetric norm on L^∞(\mathbbT) and β is a "nice" norm on L^∞(Ω,μ) where μ is a σ-finite measure on Ω. We prove a version of Beurling's invariant subspace theorem for the space L^β(μ,H^α) . Our proof uses the recent version of Beurling's theorem on H^α(\mathbbT) proved by the first author and measurable cross-section techniques. Our result significantly extends a result of H. Rezaei, S. Talebzadeh, and D. Y. Shin.

Citations

• On two problems concerning linear transformations in hilbert space

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