Sh. Chen

Landau’s theorem for certain biharmonic mappings

Abstract In this paper, we show the existence of Landau and Bloch constants for biharmonic mappings of the form L ( F ) . Here L represents the linear complex operator L = z ∂ ∂ z - z ¯ ∂ ∂ z ¯ defined on the class of complex-valued C 1 functions in the plane, and F belongs to the class of biharmonic mappings of the form F ( z ) = | z | 2 G ( z ) + K ( z ) ( | z | 1 ) , where G and K are harmonic.

Lipschitz spaces and bounded mean oscillation of harmonic mappings

In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on Lipschitz number of planar harmonic mappings in terms of bounded mean oscillation norm, which shows that the harmonic Bloch space is isomorphic to

ON HARMONIC BLOCH SPACES IN THE UNIT BALL OF ℂ n

BMO_{2}

Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings

as a Banach space. 10.1017/S0004972712000998

General Approach to Regions of Variability via Subordination of Harmonic Mappings

In this paper, our main aim is to discuss the properties of harmonic mappings in the unit ball

Bloch constant and Landau's theorem for planar p-harmonic mappings

\mathbb{B}^n

Properties of Some Classes of Planar Harmonic and Planar Biharmonic Mappings

. First, we characterize the harmonic Bloch spaces and the little harmonic Bloch spaces from

Landau's theorem for p-harmonic mappings in several variables

\mathbb{B}^n

Harmonic mappings in Bergman spaces

to

Landau–Bloch Constants for Functions in α-Bloch Spaces and Hardy Spaces

\mathbb{C}