On the optimal multilinear Bohnenblust--Hille constants

2013/02/03 by Daniel Núñez-Alarcón, D. Nunez-Alarcon, Daniel Pellegrino +9
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #math.FA

paper · pdf · doi:10.48550/arxiv.1302.0517

arxiv created 2013/02/03 · arxiv updated 2013/02/05

Abstract

The upper estimates for the optimal constants of the multilinear Bohnenblust--Hille inequality obtained in [J. Funct. Anal. 264 (2013), 429--463] are here improved to: 0.1cm enumerate For real scalars: K_n≤√(2)(n-1)^0.526322. For complex scalars: K_n≤(2)/(√π)(n-1)^0.304975.enumerate 0.1cm \noindent We also obtain sharper estimates for higher values of n. For instance, K_n<1.30379(n-1) ^0.526322 for real scalars and n>2⁸ and K_n<0.99137(n-1) ^0.304975 for complex scalars and n > 2¹⁵.

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