author = "Pellegrino, D."
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## The Bohr radius of the $n$-dimensional polydisk is equivalent to $\ sqrt {\ frac {\ log n}{n}}$

Description: We show that the Bohr radius of the polydisk $\mathbb D^n$ behaves asymptotically as $\sqrt{(\log n)/n}$. Our argument is based on a new interpolative approach to the Bohnenblust--Hille inequalities which allows us to prove that the polynomial Bohnenblust--Hille inequality is subexponential.
Language(s): Inglés

## Hölder's inequality: some recent and unexpected applications

Description: Holder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and may be considered a milestone in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and bringing new insights to the mathematical community. In this survey we show how a v...
Language(s): Inglés

## On very non-linear subsets of continuous functions

Description: In this paper we continue the study initiated by Gurariy and Quarta in 2004 on the existence of linear spaces formed, up to the null vector, by continuous functions that attain the maximum only at one point. Inserting a topological flavor to the subject, we prove that results already known for funct...
Language(s): Inglés

## Peano curves on topological vector spaces

Description: The starting point of this paper is the existence of Peano curves, that is, continuous surjections mapping the unit interval onto the unit square. From this fact one can easily construct of a continuous surjection from the real line R to any Euclidean space Rn. The algebraic structure of the set of ...
Language(s): Inglés

## On very non-linear subsets on continuous functions

Description: In this paper, we continue the study initiated by Gurariy and Quarta in 2004 on the existence of linear spaces formed, up to the null vector, by continuous functions that attain the maximum only at one point. Inserting a topological flavor to the subject, we prove that results already known for func...
Language(s): Inglés

## On the real polynomial Bohnenblust-Hille inequality

Description: Abstract. It was recently proved by Bayart et al. that the complex polynomial Bohnenblust–Hille inequality is subexponential. We show that, for real scalars, this does no longer hold. Moreover, we show that, if DR,m stands for the real Bohnenblust–Hille constant for m-homogeneous polynomials, then l...
Language(s): Inglés

## On the polynomial Hardy–Littlewood inequality

Description: We investigate the behavior of the constants of the polynomial Hardy-Littlewood inequality.
Language(s): Danés
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