Hadamard Product of Certain Classes of Functions
نویسنده
چکیده
In this paper we consider the Hadamard product ? of regular functions using the concept of subordination. Let P (A,B) denote the class of regular functions subordinated to the linear fractional transformation (1 +Az)/(1−Bz), where A+B 6= 0 and |B| ≤ 1. By P (A,B) ? P (C,D) we denote the set {f ? g : f ∈ P (A,B), g ∈ P (C,D)} . It is known ([3], [7]), that for some complex numbers A,B,C,D there exist X and Y such that P (A,B) ? P (C,D) ⊂ P (X,Y ). The purpose of this note is to find the necessary and sufficient conditions for the equality of the classes P (A,B) ? P (C,D) and P (X,Y ).
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