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

P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, M. Murillo-Arcila, J. B. Seoane-Sepúlveda

Published 2015-02-07Version 1

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.