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 4q 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.