Abstract
AbstractWe consider the class of all sense‐preserving harmonic mappings of the unit disk , where h and g are analytic with , and determine the Bohr radius if any one of the following conditions holds: h is bounded in . h satisfies the condition in with . both h and g are bounded in . h is bounded and . We also consider the problem of determining the Bohr radius when the supremum of the modulus of the dilatation of f in is strictly less than 1. In addition, we determine the Bohr radius for the space of analytic Bloch functions and the space of harmonic Bloch functions. The paper concludes with two conjectures.
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