On Harmonic $${\varvec{\nu }}$$ ν -Bloch and $${\varvec{\nu }}$$ ν -Bloch-Type Mappings

• DOI: 10.1007/s00025-018-0853-2
• Publication Date: 2018-06-12T21:17:40Z
• Authors: Gang Liu; Saminthan Ponnusamy
• Keywords: Bohr model; Subordination; Harmonic; Bloch space; Bloch wave; Bloch sphere; Subharmonic function

The aim of this paper is twofold. One of them is to introduce the class of harmonic $$\nu $$ -Bloch-type mappings as a generalization of harmonic $$\nu $$ -Bloch mappings and thereby we generalize some recent results of harmonic 1-Bloch-type mappings investigated recently by Efraimidis et al. (Complex Var Elliptic Equ 62:1081–1092, 2017). The other is to investigate some subordination principles for harmonic Bloch mappings and then establish Bohr’s theorem for these mappings and in a general setting, in some cases.