New lower bounds for the constants in the real polynomial Hardy--Littlewood inequality

The optimal Hardy--Littlewood constants for $2$-homogeneous polynomials on $\ell_{p}(\mathbb{R}^{2})$ for $2

“…In this note we obtain simple formulas for the optimal Hardy-Littlewood constants for 2-homogeneous polynomials on ℓ p (R 2 ) for all 2 < p ≤ 4. Up to now, the only known simple (explicit) formula for these constants is 2 1/2 for p = 4, due to Araujo et al [2], extending previous results of [9].…”

“…We finish the paper by remarking that our main theorem recovers the computer assisted numerical table presented in ( [2]), and also corrects the rounding errors since our estimates are exact. As a very particular case we conclude that the optimal Hardy-Littlewood constant for 2-homogeneous polynomials in ℓ 2 (R 2 ) is √ 2 (this result was obtained, numerically, as a lower bound in [9] and proved to be sharp in the aforementioned paper of Araujo et al [2]).…”