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

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

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arXiv · 1507.02984

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

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

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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 $2<p<4.$

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W. Cavalcante, D. Nunez-Alarcon, D. Pellegrino. 2015-07-10. The optimal Hardy--Littlewood constants for $2$-homogeneous polynomials on $\ell_{p}(\mathbb{R}^{2})$ for $2<p\leq4$ are $2^{2/p}$. https://arxiv.org/abs/1507.02984

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