Generalization of results about the Bohr radius for power series

Abstract

Abstract. The Bohr radius for power series of holomorphic functions mapping Reinhardt domains D ⊂ C n into a convex domain G ⊂ C is independent of the domain G.

The Bohr radius for starlike logharmonic mappings

“…If is convex, it was shown by Aizenberg [18] that the sharp Bohr radius is r = 1/3. This result includes the classical case = U.…”

Bohr’s theorem for holomorphic mappings with values in homogeneous balls

“…Also, in [18], they gave a generalisation of Bohr's theorem to holomorphic mappings of B into itself using homogeneous expansions, where B is one of the four classical domains in C n . For other generalisation of Bohr's theorem to several complex variables, see [2], [3], [4], [5], [9], [10], [11], [14], [19], [20] and [21]. Also, all references on the problem of Bohr's phenomenon can be found in the new research book [17].…”

Remarks on the Bohr and Rogosinski phenomena for power series

“…Generalization and modifications of this result can be found in [1][2][3][4][5][6][7][8][9][10][11][12][13]15,16,[19][20][21][22][23][24][25][26]28,29,31,33]. We especially point out an important, recent result contained in [20].…”