arXiv subjects

P. Jiménez-Rodríguez

Publications and source records attributed to P. Jiménez-Rodríguez.

3 recordsLinked to original sources

arXiv2015

Polynomial inequalities on the $π/4$-circle sector

A number of sharp inequalities are proved for the space ${\mathcal P}\left(^2D\left(\fracπ{4}\right)\right)$ of 2-homogeneous polynomials on ${\mathbb R}^2$ endowed with the supremum norm on the sector $D\left(\fracπ{4}\right):=\left\{e^{iθ}:θ\in \left[0,\fracπ{4}\right]\right\}$. 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 ${\mathcal P}\left(^2D\left(\fracπ{4}\right)\right)$.

math.FA↗

arXiv2015

Sharp values for the constants in the polynomial Bohnenblust-Hille inequality

In this paper we prove that the complex polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb C}^2$ is exactly $\sqrt[4]{\frac{3}{2}}$. We also give the exact value of the real polynomial Bohnenblust-Hille constant for $2$-homogeneous polynomials in ${\mathbb R}^2$. Finally, we provide lower estimates for the real polynomial Bohnenblust-Hille constant for polynomials in ${\mathbb R}^2$ of higher degrees.

math.FA↗

arXiv2013

On the real polynomial Bohnenblust-Hille inequality

It was recently proved by Bayart et al. that the complex polynomial Bohnenblust--Hille inequality is subexponential. We show that, for real scalars, this does no longer hold. Moreover, we show that, if $D_{\mathbb{R},m}$ stands for the real Bohnenblust--Hille constant for $m$-homogeneous polynomials, then $\displaystyle\lim\sup_{m}D_{\mathbb{R},m}^{1/m}=2.$

math.FA↗