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

Abstract

With the use of real-variable techniques, we construct a weight function ω on the interval [0, 2π) that is doubling and satisfies logω is a BMO function, but which is not a Muckenhoupt weight (A∞). Applications to the BMO-Teichmüller space and the space of chord-arc curves are considered.