Corpus ID: 54199544

# Polynomial Inequalities on the π/4-Circle Sector

@article{Araujo2017PolynomialIO,
title={Polynomial Inequalities on the $\pi$/4-Circle Sector},
author={G. Ara'ujo and Pablo Jim'enez-Rodr'iguez and Gustavo A. Munoz-Fern'andez and Juan B. Seoane-Sep'ulveda},
journal={arXiv: Functional Analysis},
year={2017}
}
A number of sharp inequalities are proved for the space P (2D (π/4)) of 2-homogeneous polynomials on ℝ2 endowed with the supremum norm on the sector D (π/4) := {eiθ : 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 P (2D (π/4)).
3 Citations

#### Figures from this paper

A complete study of the geometry of 2-homogeneous polynomials on circle sectors
We consider the Banach space of two homogeneous polynomials endowed with the supremum norm $$\Vert \cdot \Vert _{D(\beta )}$$ ‖ · ‖ D ( β ) over circle sectors $$D(\beta )$$ D ( β ) of all possibleExpand
Geometry of spaces of homogeneous trinomials on $${\mathbb {R}}^2$$
• Mathematics
• Banach Journal of Mathematical Analysis
• 2021
For each pair of numbers $$m,n\in {{\mathbb {N}}}$$ with $$m>n$$ , we consider the norm on $${{\mathbb {R}}}^3$$ given by \Vert (a,b,c)\Vert _{m,n}=\sup \{|ax^m+bx^{m-n}y^n+cy^m|:x,y\inExpand
Técnicas en análisis lineal (y no lineal) y aplicaciones
La presente tesis esta centrada en dos temas principales: el primero abarca el primer capitulo y el segundo se divide entre los capitulos dos y tres. En el primer capitulo estudio un problema queExpand

#### References

SHOWING 1-10 OF 27 REFERENCES
Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors
• Mathematics
• 2014
We consider the Banach space of two homogeneous polynomials endowed with the supremum norm parallel to . parallel to(D(beta)) over circle sectors D(beta) of angle beta for several values of beta isExpand
Bernstein and Markov-type inequalities for polynomials on real Banach spaces
• Mathematics
• Mathematical Proceedings of the Cambridge Philosophical Society
• 2002
In this work we generalize Markov's inequality for any derivative of a polynomial on a real Hilbert space and provide estimates for the second and third derivatives of a polynomial on a real BanachExpand
Estimates for polynomial norms on L p(μ) spaces
If L is a symmetric m -linear form on a Banach space and L^ is the associated polynomial then For special choices of Banach space this inequality can be improved. This has been done by Harris [ 5 ]Expand
A proof of Markov's theorem for polynomials on Banach spaces
Abstract Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space.Expand
An application of the Krein-Milman theorem to Bernstein and Markov inequalities
• Mathematics
• 2008
Given a trinomial of the form p(x) = ax(m) + bx(n) + c with a, b, c is an element of R, we obtain, explicitly, the best possible constant M.,,(x) in the inequality vertical bar p'(x)vertical bar <=Expand
Bernstein's inequality for multivariate polynomials on the standard simplex
• Mathematics
• 2005
The classical Bernstein pointwise estimate of the (first) derivative of a univariate algebraic polynomial on an interval has natural extensions to the multivariate setting. However, in severalExpand
Estimates on the Derivative of a Polynomial with a Curved Majorant Using Convex Techniques
• Mathematics
• 2010
A mapping phi : [-1, 1] -> [0, infinity) is a curved majorant for a polynomial p in one real variable if vertical bar p(x)vertical bar <= phi(x) for all x is an element of [-1, 1]. If P(n)(phi)(R) isExpand
Bounds on the derivatives of polynomials on Banach spaces
We generalize the classical Bernstein's and Markov's Inequalities for polynomials on any real Banach space. We also give estimates for the derivatives of homogeneous polynomials on real Banach spaces.
The Bohr radius of the $n$-dimensional polydisk is equivalent to $\sqrt{\frac{\log n}{n}} • Mathematics • 2013 We show that the Bohr radius of the polydisk$\mathbb D^n$behaves asymptotically as$\sqrt{(\log n)/n}$. Our argument is based on a new interpolative approach to the Bohnenblust--Hille inequalitiesExpand Geometry of homogeneous polynomials on non symmetric convex bodies • Mathematics • 2009 If$\Delta$stands for the region enclosed by the triangle in${\mathsf R}^2$of vertices$(0,0)$,$(0,1)$and$(1,0)$(or simplex for short), we consider the space${\mathcal P}(^2\Delta)\$ of theExpand