"Estimates for generalized Bohr radii in one and higher dimensions" by Nilanjan Das
 

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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