THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

doi:10.1007/s10473-019-0414-0

Abstract

Abstract: We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bⁿ. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, S_Ω^*(β, A, B), strong and almost spirallike mappings of type β and order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.

Key words: Biholomorphic mappings, spirallike mappings, Bergman-Hartogs domain, Roper-Suffridge operator

CLC Number:

32A30

Yanyan CUI, Hao LIU. THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS[J].Acta mathematica scientia,Series B, 2019, 39(4): 1103-1120.

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