L² estimates on chord-arc curves

Joaquim Bruna and María J. González

Vol. 190 (1999), No. 2, 225–233

DOI: 10.2140/pjm.1999.190.225

Abstract

We characterize those domains in the plane whose boundary is a chord arc curve in terms of some L² integrals, which are mainly a version of Green’s theorem. As a consequence of this we obtain a “converse" to a theorem due to Laurentiev that states that for such domains harmonic measure and arc length are A_∞ equivalent.

Milestones

Received: 1 November 1996

Revised: 5 August 1998

Published: 1 October 1999