A nontrivial closed formula for the lower bounds for the constants of the real Hardy-Littlewood inequalities

2015/04/16 by Daniel Pellegrino, Pellegrino, Daniel
Mathematics · #Advanced Harmonic Analysis Research #Analytic Number Theory Research #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1504.04207

Abstract

This note has a twofold purpose. To improve the best known lower estimates of the Hardy-Littlewood inequality for m-linear forms in ℓ_p spaces and to provide a closed formula encompassing the cases p>2m and % p=2m. Our approach is quite simpler than the previous and uses the best known constants of the Clarkson's inequalities.

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