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 ℂ2 is exactly 4√3/2. We also give the exact value of the real polynomial Bohnenblust–Hille constant for 2-homogeneous polynomials in ℝ2. Finally, we provide lower estimates for the real polynomial Bohnenblust–Hille constant for polynomials in ℝ2 of higher degrees.