Resumen de Bohr-Type Inequalities for Harmonic Mappings with a Multiple Zero at the Origin

Yong Huang, Ming Sheng Liu, Saminathan Ponnusamy

• In this paper, we first determine Bohr’s inequality for the class of harmonic mappings f=h+g¯¯¯ in the unit disk D, where either both h(z)=∑∞n=0apn+mzpn+m and g(z)=∑∞n=0bpn+mzpn+m are analytic and bounded in D, or satisfies the condition |g′(z)|≤d|h′(z)| in D∖{0} for some d∈[0,1] and h is bounded. In particular, we obtain Bohr’s inequality for the class of harmonic p-symmetric mappings. Also, we investigate the Bohr-type inequalities of harmonic mappings with a multiple zero at the origin and that most of results are proved to be sharp.