Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 36, 2011, 215-229

DAVID HOMEOMORPHISMS VIA CARLESON BOXES

Edson de Faria

University of São Paulo, Department of Mathematics
Rua do Matão 1010, CEP 05508-090, São Paulo, SP, Brazil; edson 'at' ime.usp.br

Abstract. We construct a family of examples of increasing homeomorphisms of the real line whose local quasi-symmetric distortion blows up almost everywhere, which nevertheless can be realized as the boundary values of David homeomorphisms of the upper half-plane. The construction of such David extensions uses Carleson boxes.

2000 Mathematics Subject Classification: Primary 30C62; Secondary 37F30, 26A30.

Key words: David homeomorphism, Carleson boxes, quasi-symmetric distortion, Borel-Cantelli argument.

Reference to this article: E. de Faria: David homeomorphisms via Carleson boxes. Ann. Acad. Sci. Fenn. Math. 36 (2011), 215-229.

Full document as PDF file

doi:10.5186/aasfm.2011.3613