Geodesic
Polynomial Inequalities on the π/4-Circle Sector
Journal of convex analysis, Tome 24 (2017) no. 3, pp. 927-953
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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 ${\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right)$.
Classification : 46G25, 46B28, 41A44
Mots-clés : Bernstein and Markov inequalities, unconditional constants, polarizations constants, polynomial inequalities, homogeneous polynomials, extreme points 
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     author = {G. Ara\'ujo and P. Jim\'enez-Rodr{\'\i}guez and G. A. Mu\~noz-Fern\'andez and J. B. Seoane-Sep\'ulveda},
     title = {Polynomial {Inequalities} on the {\ensuremath{\pi}/4-Circle} {Sector}},
     journal = {Journal of convex analysis},
     pages = {927--953},
     year = {2017},
     volume = {24},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a10/}
}
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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, Tome 24 (2017) no. 3, pp. 927-953. http://geodesic.mathdoc.fr/item/JCA_2017_24_3_JCA_2017_24_3_a10/