Bohr’s power series theorem in several variables
Harold P. Boas, Dmitry Khavinson · Proceedings of the American Mathematical Society · 1997
Generalizing a classical one-variable theorem of Bohr, we show that if an $n$-variable power series has modulus less than $1$ in the unit polydisc, then the sum of the moduli of the terms is less than $1$ in the polydisc of radius $1/(3\sqrt n )$.