A short communication on the constants of the multilinear Hardy--Littlewood inequality

2015/10/01 by Daniel Pellegrino, Pellegrino, Daniel
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Holomorphic and Operator Theory #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1510.00367

arxiv created 2015/10/01 · openalex publication_date 2015/10/01 · arxiv updated 2015/10/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It was recently proved that for p>2m³-4m²+2m the constants of the Hardy--Littlewood inequality for m-linear forms on ℓ_p-spaces are less than or equal to the best known estimates of respective constants of the Bohnenblust--Hille inequality. In this note we obtain upper bounds for opposite side, i.e., the constants when 2m≤ p≤2m³-4m²+2m. For these values of p our result improves previous estimates from 2014 of Araujo et al. for all m≥3.

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