# Tangential Markov inequality in ${L}^{p}$ norms

• Volume: 107, Issue: 1, page 183-193
• ISSN: 0137-6934

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## Abstract

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In 1889 A. Markov proved that for every polynomial p in one variable the inequality $||{p}^{\text{'}}{||}_{\left[-1,1\right]}{\le \left(degp\right)²||p||}_{\left[-1,1\right]}$ is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs and surfaces, which have been proved earlier for the uniform norm, can be generalized to ${L}^{p}$ norms.

## How to cite

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Agnieszka Kowalska. "Tangential Markov inequality in $L^p$ norms." Banach Center Publications 107.1 (2015): 183-193. <http://eudml.org/doc/281972>.

@article{AgnieszkaKowalska2015,
abstract = {In 1889 A. Markov proved that for every polynomial p in one variable the inequality $||p^\{\prime \}||_\{[-1,1]\} ≤ (deg p)² ||p||_\{[-1,1]\}$ is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs and surfaces, which have been proved earlier for the uniform norm, can be generalized to $L^p$ norms.},
author = {Agnieszka Kowalska},
journal = {Banach Center Publications},
keywords = {tangential Markov inequality; semialgebraic sets},
language = {eng},
number = {1},
pages = {183-193},
title = {Tangential Markov inequality in $L^p$ norms},
url = {http://eudml.org/doc/281972},
volume = {107},
year = {2015},
}

TY - JOUR
AU - Agnieszka Kowalska
TI - Tangential Markov inequality in $L^p$ norms
JO - Banach Center Publications
PY - 2015
VL - 107
IS - 1
SP - 183
EP - 193
AB - In 1889 A. Markov proved that for every polynomial p in one variable the inequality $||p^{\prime }||_{[-1,1]} ≤ (deg p)² ||p||_{[-1,1]}$ is true. Moreover, the exponent 2 in this inequality is the best possible one. A tangential Markov inequality is a generalization of the Markov inequality to tangential derivatives of certain sets in higher-dimensional Euclidean spaces. We give some motivational examples of sets that admit the tangential Markov inequality with the sharp exponent. The main theorems show that the results on certain arcs and surfaces, which have been proved earlier for the uniform norm, can be generalized to $L^p$ norms.
LA - eng
KW - tangential Markov inequality; semialgebraic sets
UR - http://eudml.org/doc/281972
ER -

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