The optimal Hardy--Littlewood constants for $2$-homogeneous polynomials on ${\ell }_p({\mathbb{R}}^2)$ for $2<p\le 4$ are $2^{2/p}$

Abstract

We show that the optimal constants for the Hardy--Littlewood inequalities for $2$-homogeneous polynomials on ${\ell }_p({\mathbb{R}}^2)$ are precisely $2^{2/p}$ for all $2<p<4.$

Cited by in corpus (1)

• Remarks on the Hardy--Littlewood inequality for $m$-homogeneous polynomials and $m$-linear forms