Multidimensional analogues of Bohr's theorem on power series

Lev Aizenberg

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


Generalizing the classical result of Bohr, we show that if an nvariable power series converges in n-circular bounded complete domain D and its sum has modulus less than 1, then the sum of the maximum of the modulii of the terms is less than 1 in the homothetic domain r = D, where (Formula Presented). This constant is near to the best one for the domain D = (z: z1 + … + zn 1).

Original languageEnglish
Pages (from-to)1147-1155
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - 1999


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