Remarks on a paper of K. Burdzy (Q1084539)

Let R be a strip region, that is, a simply connected domain containing the real axis, and let S be the unit strip \(\{\) \(z: -\infty <Re z<+\infty\), \(-<Im z<\}\). Let \(\phi\) (w) be a conformal mapping of R onto S. Recently, \textit{K. Burdzy} has derived a new criterion for the existence of a finite angular derivative for \(\phi\) at \(+\infty\). The results involve the notion of a ''Lipschitz minorant of the boundary of R'' and the proofs make extensive use of probability theory. In the paper under review, it is shown that Burdzy's results are equivalent to statements involving only classical angular derivative criteria used earlier by the authors and by K. Oikawa. They then give a complex analysis proof of Burdzy's sufficient condition for the existence of the angular derivative.