A description of $A_{\infty }$-weights for VMO

Jinsong Liu; Fei Tao; Huaying Wei

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arXiv · 2109.07363

A description of $A_{\infty }$-weights for VMO

Jinsong Liu·Fei Tao·Huaying Wei

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Abstract

We present a new characterization of Muckenhoupt $A_{\infty}$-weights whose logarithm is in $\operatorname{VMO}(\mathbb{R})$ in terms of vanishing Carleson measures on $\mathbb{R}_+^2$ and vanishing doubling weights on $\mathbb{R}$. This also gives a novel description of strongly symmetric homeomorphisms on the real line by using a geometric quantity.

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Jinsong Liu, Fei Tao, Huaying Wei. 2021-09-15. A description of $A_{\infty }$-weights for VMO. https://arxiv.org/abs/2109.07363

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