| In this thesis,we define some kinds of Roper-Suffridge operators on a special Bergman-Hartogs domain and discuss their geometric properties.It consists of two chapters.In the first chapter,we introduce the background of the development of geometric function theory in several complex variables,some definitions,notations and the main results of this thesis.In the second chapter,we focus on a special Bergman-Hartogs domain which is based on the unit disc and the unit ball.We use the known Roper-Suffridge operator on the bottom to construct the modified Roper-Suffridge operator on this special Berginan-Hartogs domain.It turned out that these oerators preserve the properties of almost spirallikeness of type β and order α,spirallikeness of type β and order α,and strongly spirallikeness of type β on the above domain under some condition,respectively.The Bergman-Hartogs domain is not holomorphicly equivalent to the unit ball,and is essentially different from the Reinhardt domain.Therefore,it is meaningful to discuss operators on this type of domain.We not only get some new content,but also improve the results of the Roper-Suffridge operator on different areas. |
