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

Banach Center Publications (2015)

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

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topAgnieszka 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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