An abstract approach to Bohr's phenomenon

In 1914 Bohr discovered that there exists r is an element of (0, 1) such th at if a power series converges in the unit disk and its sum has modulus les s than 1, then for \z\ < r the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of sev eral variables. Our aim here is to present an abstract approach to the prob lem and show that Bohr's phenomenon occurs under very general conditions.