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arXiv · 1503.06607

Polynomial inequalities on the $\pi/4$-circle sector

G. Araújo·P. Jiménez-Rodríguez·G. A. Muñoz-Fernández·J. B. Seoane-Sepúlveda
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Abstract

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 ${\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right)$.

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G. Araújo, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. 2015-03-23. Polynomial inequalities on the $\pi/4$-circle sector. https://arxiv.org/abs/1503.06607

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