Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

Abstract

In this paper we prove that the complex polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb{C}}^2$ is exactly $\sqrt[4]{\frac{3}{2}}$. We also give the exact value of the real polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb{R}}^2$. Finally, we provide lower estimates for the real polynomial Bohnenblust-Hille constant for polynomials in ${\mathbb{R}}^2$ of higher degrees.

16 pages

References in corpus (1)

• Hypercontractivity of the Bohnenblust-Hille inequality for polynomials and multidimensional Bohr radii

Cited by in corpus (2)

• Estimates on the norm of polynomials and applications
• New lower bounds for the constants in the real polynomial Hardy--Littlewood inequality