A real-variable construction with applications to BMO-Teichmüller theory

Abstract

With the use of real-variable techniques, we construct a weight function $\omega$ on the interval $[0,2\pi )$ that is doubling and satisfies $\log \omega$ is a BMO function, but which is not a Muckenhoupt weight ($A_{\infty }$). Applications to the BMO-Teichmüller space and the space of chord-arc curves are considered.

12 pages