2012/03/05 by G. A. Muñoz-Fernández, Muñoz-Fernández, G. A., D. Pellegrino +5
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA
paper · pdf · doi:10.48550/arxiv.1203.0793
This preprint does no longer exist as a single manuscript. It is now part of the preprint entitled "The optimal asymptotic hypercontractivity constant of the real polynomial Bohnenblust-Hille inequality is 2" (arXiv reference 1209.4632)
arxiv created 2013/09/11 · arxiv updated 2013/09/12
The Bohnenblust--Hille (polynomial and multilinear) inequalities were proved in 1931 in order to solve Bohr's absolute convergence problem on Dirichlet series. Since then these inequalities have found applications in various fields of analysis and analytic number theory. The control of the constants involved is crucial for applications, as it became evident in a recent outstanding paper of Defant, Frerick, Ortega-Cerdá, Ouna"ıes and Seip published in 2011. The present work is devoted to obtain lower estimates for the constants appearing in the Bohnenblust--Hille polynomial inequality and some of its variants. The technique that we introduce for this task is a combination of the Krein--Milman Theorem with a description of the geometry of the unit ball of polynomial spaces on ℓ2_∞.