The Sidon constant for homogeneous polynomials

2009/03/08 by Joaquim Ortega‐Cerdà, Joaquim Ortega-Cerdà, Myriam Ounaïès +5 · 1 citation
Mathematics · #32A05 #43A46 #Advanced Banach Space Theory #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32A05 #msc:43A46

paper · pdf · doi:10.48550/arxiv.0903.1455

arxiv created 2009/03/08 · openalex publication_date 2009/03/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/03

Abstract

The Sidon constant for the index set of nonzero m-homogeneous polynomials P in n complex variables is the supremum of the ratio between the l¹ norm of the coefficients of P and the supremum norm of P in Dⁿ. We present an estimate which gives the right order of magnitude for this constant, modulo a factor depending exponentially on m. We use this result to show that the Bohr radius for the polydisc Dⁿ is bounded from below by a constant times sqrt((log n)/n).

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• The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive

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