DOI: 10.68381/jca24055 ISSN: 0944-6532
Polynomial Inequalities on the π/4-Circle Sector
Gustavo da Silva Araújo, Pablo Jiménez-Rodríguez, Gustavo A. Muñoz-Fernández, Juan B. Seoane-Sepúlveda
A number of sharp inequalities are proved for the space
{\mathcal P}\left(^2D\left(\frac{\pi}{4}\right)\right)
P
(
2
D
(
π
4
)
)
of 2-homogeneous polynomials on
{\mathbb R}^2
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\}
D
(
π
4
)
:
=
{
e
i
θ
:
θ
∈
[
0
,
π
4
]
}
. 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)
P
(
2
D
(
π
4
)
)
.