Tangential Markov inequality in $L^p$ norms

• Autorzy: Agnieszka Kowalska
• Języki publikacji: EN

Abstrakty

EN

In 1889 A. Markov proved that for every polynomial p in one variable the inequality $||p'||_{[-1,1]} ≤ (deg p)² ||p||_{[-1,1]}$ 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.

Kategorie tematyczne

• 14P05: Real algebraic sets
• 14P10: Semialgebraic sets and related spaces
• 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)
• 41A25: Rate of convergence, degree of approximation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2015
• Tom: 107
• Numer: 1
• Strony: 183-193

Daty

wydano

2015

Twórcy

autor

Agnieszka Kowalska

• Institute of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, Poland

Identyfikatory

DOI

10.4064/bc107-0-13