On $μ$-conformal homeomorphisms and boundary correspondence
Vladimir Ya. Gutlyanskiĭ, Ken-ichi Sakan, Toshiyuki Sugawa · arXiv (Cornell University) · 2011
We study the boundary correspondence under $μ$-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.