Annales Academić Scientiarum Fennicć
Mathematica
Volumen 33, 2008, 241-260

ON BOUNDARY HOMEOMORPHISMS OF TRANS-QUASICONFORMAL MAPS OF THE DISK

Saeed Zakeri

Queens College and Graduate Center of CUNY, Department of Mathematics
65-30 Kissena Blvd., Flushing, New York 11367, U.S.A.; saeed.zakeri 'at' qc.cuny.edu

Abstract. This paper studies boundary homeomorphisms of trans-quasiconformal maps of the unit disk. Motivated by Beurling-Ahlfors's well-known quasisymmetry condition, we introduce the "scalewise" and "pointwise" distortions of a circle homeomorphism and formulate conditions in terms of each that guarantee the existence of a David extension to the disk. These constructions are also used to obtain extension results for maps with subexponentially integrable dilatation as well as BMO-quasiconformal maps of the disk.

2000 Mathematics Subject Classification: Primary 30C62, 37F30.

Reference to this article: S. Zakeri: On boundary homeomorphisms of trans-quasiconformal maps of the disk. Ann. Acad. Sci. Fenn. Math. 33 (2008), 241-260.

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