An estimate for spherically p-valent functions

نویسنده

  • A. Eremenko
چکیده

This class is related to mean p-valent holomorphic functions as defined in [1]. Theorem 1. The family of all spherically p-valent functions in a region D is quasinormal of order p in D. Proof. We may assume without loss of generality that D is the unit disc. Let fn be a sequence of spherically p-valent functions. Write fn = gn/hn so that gn and hn have no common zeros. Let un = log √ |gn|2 + |hn|2. Then un are positive subharmonic functions, and ∆un = 4(f n ) 2

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تاریخ انتشار 1998