On the real polynomial Bohnenblust-Hille inequality

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 $D_{\mathbb{R},m}$ stands for the real Bohnenblust--Hille constant for $m$-homogeneous polynomials, then $\lim \underset{m}{\sup }{D}_{\mathbb{R},m}^{1/m}=2.$

7 pages; Replaced to an improved version due to some recent advances

References in corpus (5)

• The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive
• The Bohr radius of the $n$-dimensional polydisk is equivalent to $\sqrt{\frac{\log n}{n}}$
• Hypercontractivity of the Bohnenblust-Hille inequality for polynomials and multidimensional Bohr radii
• There exist multilinear Bohnenblust-Hille constants $(C_n{)}_{n=1}^{\infty }$ with $\underset{n\to \infty }{\lim }(C_{n+1}-C_n)=0.$
• A geometric technique to generate lower estimates for the constants in the Bohnenblust--Hille inequalities

Cited by in corpus (2)

• A note on the hypercontractivity of the polynomial Bohnenblust--Hille inequality
• On the polynomial Hardy--Littlewood inequality