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In this article, we study the multi-dimensional Bohr radii of holomorphicfunctions defined on the Banach sequence spaces with values in the Banachspaces. For the case of finite dimensional Banach spaces, we exhibit the exactasymptotic growth of the Bohr radius. To achieve our goal in the finite case,we use $\ell_{p'}$-summability of certain coefficients of a given polynomial interms of its uniform norm on $\ell_p^n$. The infinite case is handled using thetechniques developed in recent years from the work of Defant, Maestre andSchwarting. We crucially use several properties of the symmetric $M$-linearmapping associated with a homogeneous polynomial of degree $M$ in our analysis.Furthermore, we study the bounds of the arithmetic Bohr radius of Banachspace-valued holomorphic functions defined on the Banach sequence spaces, whichgeneralises the work of Defant, Maestre, and C. Prengel in this direction.

Multi-dimensional Bohr radii of Banach space valued holomorphic functions