Estimates for generalized Bohr radii in one and higher dimensions

Abstract In this article, we study a generalized Bohr radius $R_{p, q}(X), p, q\in [1, \infty )$ defined for complex Banach space X . particular, determine the exact value of q}(\mathbb {C})$ cases (i) $p, 2]$ , (ii) $p\in (2, ), and (iii) [2, Moreover, consider an n -variable version q}^n(X)$ quantity q}(X)$ q}^n(\mathcal {H})$ infinite-dimensional Hilbert $\mathcal {H}$ precise asymptotic as $n\to $ finite-dimensional We also multidimensional analog related concept called p -Bohr radius. To be specific, obtain -dimensional bounded complex-valued functions, in vector-valued case, provide lower estimate same, which is independent