Bohr radius for locally univalent harmonic mappings

We consider the class of all sense-preserving harmonic mappings f=h+g of the unit disk D, where h and g are analytic with 𝑔g(0) = 0,, and determine the Bohr radius if any one of the following conditions holds: 1.h is bounded in D. 2.h satisfies the condition Re ℎ(z𝑧) ≤ 1 in D with ℎ(0) > 0. 3.both h and g are bounded in D. 4.h is bounded and g′(0) = 0.. We also consider the problem of determining the Bohr radius when the supremum of the modulus of the dilatation of f in D is strictly less than 1. In addition, we determine the Bohr radius for the space B of analytic Bloch functions and the space BH of harmonic Bloch functions. The paper concludes with two conjectures.