Abstract

A number of sharp inequalities are proved for the space P(2D(π4)){\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right) of 2-homogeneous polynomials on R2{\mathbb R}^2 endowed with the supremum norm on the sector D(π4):={eiθ:θ∈[0,π4]}D\left(\frac{\pi}{4}\right):= \left\{e^{i\theta}:\theta\in \left[0,\frac{\pi}{4}\right]\right\}. Among the main results we can find sharp Bernstein and Markov inequalities and the calculation of the polarization constant and the unconditional constant of the canonical basis of the space P(2D(π4)){\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right).

Author information

Contact details are reproduced from the original publication and may be historical.

Gustavo da Silva Araújo

Unidade Acadêmica de Ciências Exatas e da Natureza, Centro de Formação de Professores, Universidade Federal de Campina Grande, Cajazeiras, PB 58900-000, Brazil

gdasaraujo@gmail.com

Pablo Jiménez-Rodríguez

Dep. de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain

pablo.jimenez.rod@gmail.com

Gustavo A. Muñoz-Fernández

Dep. de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid

gustavo_fernandez@mat.ucm.es

Juan B. Seoane-Sepúlveda

Dep. de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid

jseoane@mat.ucm.es

Keywords

  • Bernstein and Markov inequalities
  • unconditional constants
  • polarizations constants
  • polynomial inequalities
  • homogeneous polynomials
  • extreme points

Mathematics Subject Classification

46G25; 46B28, 41A44

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Suggested citation

G. Araújo, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. “Polynomial Inequalities on the π/4-Circle Sector.” Journal of Convex Analysis 24 (2017), No. 3, 927–953. https://doi.org/10.68381/jca24055

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press.