The Bohr radius of the $n$-dimensional polydisk is equivalent to $\sqrt{\frac{\log n}{n}}$

Abstract

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.

The introduction was expanded and some misprints corrected

References in corpus (1)

• The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive

Cited by in corpus (7)

• On the upper bounds for the constants of the Hardy-Littlewood inequality
• Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators
• On the real polynomial Bohnenblust-Hille inequality
• Polynomial inequalities on the $\pi /4$-circle sector
• Absolutely summing multilinear operators via interpolation
• On the polynomial Hardy--Littlewood inequality
• A subexponential vector-valued Bohnenblust-Hille type inequality