Wyniki wyszukiwania

1

Tangential Markov inequality in $L^p$ norms

100%

Kowalska A.

Banach Center Publications

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2015

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tom 107

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nr 1

183-193

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.

2

Tangential Markov inequalities on semialgebraic curves and some semialgebraic surfaces

100%

Kowalska A.

Annales Polonici Mathematici

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2012

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tom 106

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nr 1

215-222

EN

We give another proof of the fact that any semialbraic curve admits a tangential Markov inequality. We establish this inequality on semialgebraic surfaces with finitely many singular points.

3

Sets with the Bernstein and generalized Markov properties

63%

Baran M., Kowalska A.

Annales Polonici Mathematici

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2014

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tom 111

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nr 3

259-270

EN

It is known that for $C^{∞}$ determining sets Markov's property is equivalent to Bernstein's property. We are interested in finding a generalization of this fact for sets which are not $C^{∞}$ determining. In this paper we give examples of sets which are not $C^{∞}$ determining, but have the Bernstein and generalized Markov properties.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Banach Center Publications

3 Kowalska A.

1 Baran M.

1 2015

1 2014

1 2012

Tangential Markov inequality in $L^p$ norms

Tangential Markov inequalities on semialgebraic curves and some semialgebraic surfaces

Sets with the Bernstein and generalized Markov properties