Estimates for generalized Bohr radii in one and higher dimensions

Article Type

Research Article

Publication Title

Canadian Mathematical Bulletin

Abstract

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

First Page

682

Last Page

699

DOI

https://10.4153/S0008439522000674

Publication Date

1-1-2023

Comments

Open Access, Green

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