A description of 𝐴_{∞}-weights for VMO

Abstract

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