On harmonic bloch and normal functions

Ozturk M., Yalcin S.

Indian Journal of Pure and Applied Mathematics, vol.36, no.8, pp.407-416, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 8
  • Publication Date: 2005
  • Journal Name: Indian Journal of Pure and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.407-416
  • Bursa Uludag University Affiliated: Yes

Abstract

Let f = h + ḡ be a harmonic univalent and sense preserving function on the unit disk, where h and g are analytic. We give the definition of a normal harmonic function. The necessary and sufficient conditions for f = h + ḡ to be Bloch or normal are determined. The sharp upper bound for | f (z) | is obtained whenever f = h + ḡ is a Bloch function. We obtain sharp estimates for the normality order of f when f maps the unit disk onto the unit disk.