Boundary behavior of \(\mu\)-homeomorphisms (Q1885659)

Let \(f\) be a sense preserving homeomorphism of the upper half plane \(H\) into \({\mathbb C}\) satisfying the Beltrami equation \(f_{\overline z} = \mu (z)f_z\) with \(| \mu| _{\infty} < 1\) in every compact subset of \(H\). The authors present conditions such that \(f(H) \neq C\) and \(f\) has a homeomorphic extension to \(\overline H\). The conditions involving regularity of \(| \mu| \) and \(\text{ arg}\;\mu\) have a local character and they are different from the BMO--type conditions for \(\mu\), see [\textit{G. David}, Ann. Acad. Sci. Fenn., Ser. A I Math. 13, No. 1, 25--70 (1983; Zbl 0619.30024)].