Boundary behavior of derivatives of conformal mappings of simply-connected domain / E. P. Dolzhenko, S. V. Kolesnikov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2014. № 5. P. 29-35 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 0].

Conformal mappings of simply connected domains G on a disc or a halfplane are considered in the case when boundaries consist of smooth boundary arcs Γ reachable from inside of G. Sufficient conditions for existence of angular limit of the derivative of such mappings and its boundedness at some given boundary point are found. A sufficient condition of existence of a bounded derivative on the region's boundary is given as a corollary.

Key words: conformal maps, angular limit, Lipschitz's condition.