On $μ$-conformal homeomorphisms and boundary correspondence

Details On $μ$-conformal homeomorphisms and boundary correspondence On $μ$-conformal homeomorphisms and boundary correspondence

2011-02-24

arxiv.org/abs/1102.4987v1

Mathematics

Complex Variables

15 pages

Scientific paper

We study the boundary correspondence under $\mu$-homeomorphisms $f$ of the open upper half-plane onto itself. Sufficient conditions are given for $f$ to admit a homeomorphic extension to the closed half-plane with prescribed boundary regularity. The proofs are based on the modulus estimates for semiannuli in terms of directional dilatations of $f$ which might be of independent interest.

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