Journal of Convex Analysis 24 (2017), No. 3, 927--953
Copyright Heldermann Verlag 2017
Polynomial Inequalities on the π/4-Circle Sector
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
[Abstract-pdf]
A number of sharp inequalities are proved for the space ${\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right)$ of 2-homogeneous polynomials on ${\mathbb R}^2$ endowed with the supremum norm on the sector $D\left(\frac{\pi}{4}\right) := \left\{e^{i\theta}:\theta\in \left[0,\frac{\pi}{4}\right]\right\}$. 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 ${\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right)$.
Keywords: Bernstein and Markov inequalities, unconditional constants, polarizations constants, polynomial inequalities, homogeneous polynomials, extreme points.
MSC: 46G25; 46B28, 41A44
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