The optimal Hardy--Littlewood constants for $2$-homogeneous polynomials on $\ell_{p}(\mathbb{R}^{2})$ for $2<p\leq4$ are $2^{2/p}$

D. Nunez-Alarcon; D. Pellegrino; W. Cavalcante

arxiv: 1507.02984 · v2 · pith:QSN7DNBKnew · submitted 2015-07-10 · 🧮 math.FA

The optimal Hardy--Littlewood constants for 2-homogeneous polynomials on ell_(p)(mathbb{R}²) for 2<pleq4 are 2^(2/p)

W. Cavalcante , D. Nunez-Alarcon , D. Pellegrino This is my paper

classification 🧮 math.FA

keywords constantshardy--littlewoodhomogeneousmathbboptimalpolynomialsinequalitiesleq4

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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 $2<p<4.$

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The optimal Hardy--Littlewood constants for 2-homogeneous polynomials on ell_(p)(mathbb{R}²) for 2<pleq4 are 2^(2/p)

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