Weighted composition operators on the class of subordinate functions

Abstract

In this article, we study the weighted composition operators preserving the class ${\mathcal{P}}_{\alpha }$ of analytic functions subordinate to $\frac{1+\alpha z}{1-z}$ for $|\alpha |\le 1,\alpha \ne -1$. Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.

11 pages; To appear in Rocky Mountain Journal of Mathematics (exclusion of the results of Section 6)