On multidimensional Bohr radius of finite dimensional Banach spaces

In this paper, we improve the lower estimate of multidimensional Bohr radius for unit ball of ${\mathrm{\ell }}_q^n$-spaces ($1\le q\le \mathrm{\infty }$) for bounded holomorphic functions with values in finite dimensional complex Banach spaces. The new estimate provides the improved lower bound for the Bohr radius which was previously given by Defant, Maestre, and Schwarting [Adv. Math. 231 (2012), 2837–2857].