Lipschitz Spaces and Bounded Mean Oscillation of Harmonic Mappings

Abstract

We first study the bounded mean oscillation of planar harmonic mappings. Then we establish a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings. Finally, we obtain sharp estimates on the Lipschitz number of planar harmonic mappings in terms of the bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to BMO 2 as a Banach space.2010 Mathematics subject classification: primary 30H10, 30H30; secondary 30C20, 30C45.

Coefficient Estimates and Bloch’s Constant in Some Classes of Harmonic Mappings

“…Recently, the Bloch's constant was studied by many authors, see, for example [3,4,19]. Very interesting results in this direction were obtained in [5][6][7]18,20,22]. Our aim is to determine the bounds for the Bloch's constant in the classes S α and S α .…”