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

We present a new characterization of Muckenhoupt A_{\infty }-weights whose logarithm is in vanishing mean oscillation (\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. [ABSTRACT FROM AUTHOR]