A remark on Bohr's inequality

By Enrico Bombieri, Jean Bourgain. 2004

94 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d5c320ce4156f8c2120222e2d8ab0397c6bee2d0

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On the Bohr inequality with a fixed zero coefficient (2019, background): “’s inequality stated above and further related investigations, we refer the reader to the recent survey articles on the Bohr radius from [1, 17], [16, Chapter 8], and the references therein. See also [10, 11]. In particular, Boas and Khavinson [8], Aizenberg [2, 3], and Aizenberg and Tarkhanov [4] h”
The p-Bohr radius of a Banach space (2016, background): “Several authors (see [4,11,12,19,20,28]) have found some other extensions of Bohr’s estimate in different directions.”
On Kahane's ultraflat polynomials (2009, background): “Proofs of Theorems 2 and 3 We choose ψ as in [4], namely”
Sharp Bohr type inequality (2020, background): “[37] and [38]). Also, we would to recall that Bombieri [13] proved the following which gives an upper bound on the growth of Bf(r): supBf(r) = 3− p 8(1− r2) r , 1/3 ≤ r≤ 1/ √ 2. Bombieri and Bourgain [14] investigated asymptotical behaviour of Bohr’s sums as r→ 1. In fact, they constructed an, and b”
Improved version of Bohr's inequality (2018, result): “[5] E. Bombieri, J. Bourgain, A remark on Bohr’s inequality, Int.”
Some Remarks on the Algebra of Bounded Dirichlet Series (2008, background): “Observe that Theorem 2.5 shows that there is no analogy of the extension by Bombieri-Bourgain of the Bohr Theorem 1.5: here, for σ > 1 2 , we have ∞ ∑ 1 |an|n−σ ≤ √ √ √ √ ∞ ∑ 1 |an|2 √ ζ(2σ), (2.7) and we might expect, as in Bombieri and Bourgain, that this is essentially optimal and that things exp”