On the real polynomial Bohnenblust-Hille inequality

J. R. Campos; P. Jiménez-Rodríguez; G. A. Muñoz-Fernández; D. Pellegrino; J. B. Seoane-Sepúlveda

On the real polynomial Bohnenblust-Hille inequality

Functional Analysis 2013-12-06 v7

Authors: J. R. Campos , P. Jiménez-Rodríguez , G. A. Muñoz-Fernández , D. Pellegrino , J. B. Seoane-Sepúlveda

Abstract

It was recently proved by Bayart et al. that the complex polynomial Bohnenblust--Hille inequality is subexponential. We show that, for real scalars, this does no longer hold. Moreover, we show that, if $D_{\mathbb{R},m}$ stands for the real Bohnenblust--Hille constant for $m$ -homogeneous polynomials, then $\displaystyle\lim\sup_{m}D_{\mathbb{R},m}^{1/m}=2.$

Keywords

polynomial theory

Cite

@article{arxiv.1209.4632,
  title  = {On the real polynomial Bohnenblust-Hille inequality},
  author = {J. R. Campos and P. Jiménez-Rodríguez and G. A. Muñoz-Fernández and D. Pellegrino and J. B. Seoane-Sepúlveda},
  journal= {arXiv preprint arXiv:1209.4632},
  year   = {2013}
}

Comments

7 pages; Replaced to an improved version due to some recent advances

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