A note on sharp multivariate Bernstein- and Markov-type inequalities

DOI10.1016/j.jat.2022.105847OpenAlexW4310067846MaRDI QIDQ2680833

Michael I. Ganzburg

Publication date: 4 January 2023

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.12480

zbMATH Keywords

entire functions of exponential typealgebraic polynomialsmultivariate Bernstein-type inequalitymultivariate Markov-type inequality

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Inequalities involving derivatives and differential and integral operators (26D10) Harmonic analysis on Euclidean spaces (42-XX) Approximations and expansions (41-XX)

Cites Work

• Nikol'skii inequalities for Lorentz spaces
• Multidimensional Bernstein-type inequalities
• Multivariate Bernstein and Markov inequalities
• On Bernstein and Markov-type inequalities for multivariate polynomials on convex bodies
• Bernstein type theorems for compact sets in \(\mathbb{R}^ n\) revisited
• A Markov inequality in several dimensions
• Sharp constants of approximation theory. I. Multivariate Bernstein-Nikolskii type inequalities
• On sharp constants in Bernstein-Nikolskii inequalities
• Extremal radii, diameter and minimum width in generalized Minkowski spaces
• Sharp constants of approximation theory. V. An asymptotic equality related to polynomials with given Newton polyhedra
• Monge-Ampère measures for convex bodies and Bernstein-Markov type inequalities
• Homogeneous polynomials and extensions of Hardy-Hilbert's inequality
• THE THEOREMS OF JACKSON AND BERNSTEIN INR^m
• Bounds on the derivatives of polynomials on Banach spaces
• On multivariate polynomials with largest gradients on convex bodies
• Uniqueness of Markov-extremal polynomials on symmetric convex bodies
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