Multivariate Bernstein and Markov inequalities

DOI10.1016/0021-9045(92)90061-RzbMath0773.41016MaRDI QIDQ1198157

Z. Ditzian

Publication date: 16 January 1993

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

zbMATH Keywords

Markov inequalityBernstein inequalities

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63)

Related Items (18)

Generalized pointwise Hölder spaces defined via admissible sequences ⋮ Strong converse inequalities for the weighted multivariate Bernstein-Durrmeyer operator on the simplex via multipliers ⋮ The equivalence relations between the Ditzian-Totik moduli of smoothness and best polynomial approximation in the Besov spaces ⋮ WEIERSTRASS' THEOREM IN THE TWENTIETH CENTURY: A SELECTION ⋮ Exponential meshes and \(\mathcal{H}\)-matrices ⋮ Weighted \(L_p\) Markov factors with doubling weights on the ball ⋮ A note on sharp multivariate Bernstein- and Markov-type inequalities ⋮ \(L_p\) Bernstein type inequalities for star like Lip \(\alpha\) domains ⋮ Bernstein inequality on conic domains and triangles ⋮ Big data interpolation using functional representation ⋮ Best polynomial and Durrmeyer approximation in \(L_ p(S)\) ⋮ An \(\mathcal{O}(p^3)\) \(hp\)-version FEM in two dimensions: preconditioning and post-processing ⋮ Ul'yanov-type inequality for bounded convex sets in \(\mathbb R^d\) ⋮ The equivalence relations between the best approximation and linear operators approximation in a Besov space ⋮ \(K\)-functionals and multivariate Bernstein polynomials ⋮ Solving PDEs with Hermite Interpolation ⋮ Unnamed Item ⋮ Preconditioning the Mass Matrix for High Order Finite Element Approximation on Tetrahedra

Cites Work

• Unnamed Item
• Markov's inequality and the existence of an extension operator for \(C^{\infty}\) functions
• Markov's inequality and \(C^{\infty}\) functions on sets with polynomial cusps
• Markov's inequality on locally Lipschitzian compact subsets of \({\mathbb{R}}^ N\) in \(L^ p\)-spaces
• Bernstein's inequality in \(L^p\) for \(O<p<1\)
• Polynomial inequalities on general subsets of $R^N$
• Orthogonal polynomials
• Approximation et interpolation des fonctions différentiables de plusieurs variables
• ON INTEGRAL INEQUALITIES FOR TRIGONOMETRIC POLYNOMIALS AND THEIR DERIVATIVES

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