On harmonic univalent functions

Abstract

Let f = h + ğ be a harmonic, univalent and orientation-preserving function on the unit disk, where h and g are analytic. We show that log|h(e^it)| and log|g(e^it)| are BMO when some Bloch conditions are satisfied.

Keywords:

• Harmonic functions
• univalent functions
• Bloch functions
• BMO functions

1991 AMS Subject Classification:

• Primary 30C99
• Secondary 30C62
• 31A20