Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Some Remarks Concerning Quasiconformal Extensions in Several Complex Variables | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 690932 16 pages doi 2008 690932 Research Article Some Remarks Concerning Quasiconformal Extensions in Several Complex Variables Paula Curt1 and Gabriela Kohr2 1 Department of Statistics Forecasts and Mathematics Faculty of Economics and Business Administration Babe -Bolyai University 58-60 Teodor Mihali Street 400591 Cluj-Napoca Romania 2 Department of Mathematics Faculty of Mathematics and Computer Science Babe -Bolyai University 1 M. Kogalniceanu Street 400084 Cluj-Napoca Romania Correspondence should be addressed to Gabriela Kohr gkohr@ Received 29 January 2008 Accepted 27 May 2008 Recommended by Ramm Mohapatra Let B be the unit ball in Cn with respect to the Euclidean norm. In this paper we obtain a sufficient condition for a normalized quasiregular mapping f e H B to be extended to a quasiconformal homeomorphism of R2n onto itself. In the last section we consider the asymptotical case of this result and we obtain certain applications. Copyright 2008 P. Curt and G. Kohr. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Becker 1 proved that if 0 q 1 and f is a holomorphic function on the unit disc U which satisfies the condition zf z __q f z s 1 z 2 z e U then f is univalent on U and extends to a quasiconformal homeomorphism of R2 onto itself. This result was generalized by Pfaltzgraff 2 cf. 3 to several complex variables. He proved that if 0 q 1 and f e H B is a quasiregular mapping which satisfies the condition 1 - z 2 Df z -1D2f z Cz - q z e B then f is biholomorphic on B and extends to a quasiconformal homeomorphism of R2n onto itself. 2 Journal of Inequalities and Applications Recently the problem of quasiconformal extensions for quasiregular .
