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arXiv · 1611.00357

An Extension of the Chen-Beurling-Helson-Lowdenslager Theorem

Haihui Fan·Don Hadwin·Wenjing Liu
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Abstract

Yanni Chen extended the classical Beurling-Helson-Lowdenslager Theorem for Hardy spaces on the unit circle $\mathbb{T}$ defined in terms of continuous gauge norms on $L^{\infty}$ that dominate $\Vert\cdot\Vert_{1}$. We extend Chen's result to a much larger class of continuous gauge norms. A key ingredient is our result that if $\alpha$ is a continuous normalized gauge norm on $L^{\infty}$, then there is a probability measure $\lambda$, mutually absolutely continuous with respect to Lebesgue measure on $\mathbb{T}$, such that $\alpha\geq c\Vert\cdot\Vert_{1,\lambda}$ for some $0<c\leq1.$

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Haihui Fan, Don Hadwin, Wenjing Liu. 2016-11-01. An Extension of the Chen-Beurling-Helson-Lowdenslager Theorem. https://arxiv.org/abs/1611.00357

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