English

A simple proof that the power $\frac{2m}{m+1}$ in the Bohnenblust--Hille inequalities is sharp

Functional Analysis 2012-07-12 v1
Authors: Daniel Nuñez-Alarcón , Daniel Pellegrino
View on arXiv ↗ PDF ↗

Abstract

The power 2mm+1\frac{2m}{m+1} in the polynomial (and multilinear) Bohnenblust--Hille inequality is optimal. This result is well-known but its proof highly nontrivial. In this note we present a quite simple proof of this fact.

Keywords

bohnemblust--hille inequality polynomial inequalities multilinear forms sharp exponent optimality

Cite

@article{arxiv.1207.2662,
  title  = {A simple proof that the power $\frac{2m}{m+1}$ in the Bohnenblust--Hille inequalities is sharp},
  author = {Daniel Nuñez-Alarcón and Daniel Pellegrino},
  journal= {arXiv preprint arXiv:1207.2662},
  year   = {2012}
}

Comments

This note will be later incorporated in another preprint

Related papers

View all related →
Functional Analysis · Mathematics
Sharp generalizations of the multilinear Bohnenblust--Hille inequality
N. Albuquerque, F. Bayart, D. Pellegrino, J. Seoane-Sepulveda
2015-10-01
Functional Analysis · Mathematics
A note on the hypercontractivity of the polynomial Bohnenblust--Hille inequality
Daniel Pellegrino
2013-01-03
Functional Analysis · Mathematics
Some improvements on the constants for the real Bohnenblust-Hille inequality
Daniel Pellegrino, Juan B. Seoane-Sepúlveda
2010-10-05
Functional Analysis · Mathematics
Complex polynomial Bohnenblust--Hille inequality with polynomial bounds
Diana Marcela Serrano Rodríguez, Fernando Cabral Alves
2019-10-08
Functional Analysis · Mathematics
On the constants of the Bohnenblust-Hille inequality and Hardy--Littlewood inequalities
Gustavo Araujo, Daniel Pellegrino
2014-08-07
Functional Analysis · Mathematics
On the real polynomial Bohnenblust-Hille inequality
J. R. Campos, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, D. Pellegrino +1
2013-12-06
Functional Analysis · Mathematics
New upper bounds for the constants in the Bohnenblust-Hille inequality
Daniel Pellegrino, Juan B. Seoane-Sepúlveda
2011-08-02
Functional Analysis · Mathematics
Bohnenblust-Hille inequalities for Lorentz spaces via interpolation
Andreas Defant, Mieczysław Mastyło
2015-08-25
Functional Analysis · Mathematics
A note on the polynomial Bohnenblust-Hille inequality
Daniel Nuñez-Alarcón
2012-08-31
Functional Analysis · Mathematics
Remarks on the Bohnenblust--Hille inequalities
Djair Paulino, Daniel Pellegrino, Joedson Santos
2020-04-07
Functional Analysis · Mathematics
Bohnenblust--Hille inequality for polynomials whose monomials have uniformly bounded number of variables
Mariana Maia, Tony Nogueira, Daniel Pellegrino
2018-04-02
Complex Variables · Mathematics
The Bohnenblust--Hille inequality for homogeneous polynomials is hypercontractive
Andreas Defant, Leonhard Frerick, Joaquim Ortega-Cerdà, Myriam Ounaïes +1
2011-10-06
Functional Analysis · Mathematics
On the optimal multilinear Bohnenblust--Hille constants
D. Nunez-Alarcon, D. Pellegrino, J. B. Seoane-Sepulveda, D. M. Serrano-Rodriguez
2013-02-05
Functional Analysis · Mathematics
The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal
Diogo Diniz, G. A. Muñoz-Fernández, Daniel Pellegrino, J. B. Seoane-Sepúlveda
2012-08-30
Functional Analysis · Mathematics
Sharp values for the constants in the polynomial Bohnenblust-Hille inequality
P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, M. Murillo-Arcila, J. B. Seoane-Sepúlveda
2015-02-10
Functional Analysis · Mathematics
Towards sharp Bohnenblust--Hille constants
Daniel Pellegrino, Eduardo Teixeira
2018-04-03
Functional Analysis · Mathematics
The optimal multilinear Bohnenblust-Hille constants: a computational solution for the real case
F. V. Costa Júnior
2019-03-20
Functional Analysis · Mathematics
A note on the Bohnenblust--Hille inequality for multilinear forms
J. Santos, T. Velanga
2016-04-05
Functional Analysis · Mathematics
The optimal constants of the mixed $\left( \ell_{1},\ell _{2}\right) $-Littlewood inequality
Daniel Pellegrino
2015-10-01
Functional Analysis · Mathematics
On the optimality of the hypercontractivity of the complex Bohnenblust--Hille inequality
J. R. Campos, G. A. Muñoz-Fernández, D. Pellegrino, J. B. Seoane-Sepúlveda
2015-02-13
Functional Analysis · Mathematics
Lower bounds for the constants in the Bohnenblust-Hille inequality: the case of real scalars
Diogo Diniz, Gustavo Muñoz-Fernández, Daniel Pellegrino, Juan B. Seoane-Sepúlveda
2015-10-01
Functional Analysis · Mathematics
A geometric technique to generate lower estimates for the constants in the Bohnenblust--Hille inequalities
G. A. Muñoz-Fernández, D. Pellegrino, J. Ramos Campos, J. B. Seoane-Sepúlveda
2013-09-12
Functional Analysis · Mathematics
When are the Hardy-Littlewood inequalities contractive?
W. V. Cavalcante, T. Nogueira, D. M. Pellegrino, J. Santos +1
2018-04-02
Functional Analysis · Mathematics
Hypercontractivity of the Bohnenblust-Hille inequality for polynomials and multidimensional Bohr radii
Andreas Defant, Leonhard Frerick
2009-03-20
Functional Analysis · Mathematics
On the multilinear Bohnenblust--Hille constants: complex versus real case
J. R. Campos, D. Nunez-Alarcon, D. Pellegrino, J. B. Seoane-Sepulveda +1
2013-10-08