Carleson measures and chord-arc curves

TL;DR

This paper investigates properties of Carleson measures and their invariance under certain operators, and explores the complex structure of quotient spaces of chord-arc curves, extending previous work by Semmes and Zinsmeister.

Contribution

It advances the understanding of Carleson measures, including vanishing measures, and establishes a natural complex structure on a quotient space of chord-arc curves.

Findings

Carleson measures are invariant under pull-back and push-forward operators.

Vanishing Carleson measures exhibit similar invariance properties.

A natural complex structure is constructed on a quotient space of chord-arc curves.

Abstract

Following Semmes and Zinsmeister, we continue the study of Carleson measures and their invariance under pull-back and push-forward operators. We also study the analogous statements for vanishing Carleson measures. As an application, we show that some quotient space of the space of chord-arc curves has a natural complex structure.