Точное неравенство Джексона в $L_p(\mathbb R^d)$ с весом Данкля

DOI10.4213/mzm12387zbMath1440.41009OpenAlexW2941997128MaRDI QIDQ5239664

R. A. Veprintsev

Publication date: 22 October 2019

Published in: Matematicheskie Zametki (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/cheb411

zbMATH Keywords

dihedral groupmodulus of continuityJackson inequalitybest approximationEuclidean sphereJackson constant\(\kappa\)-spherical harmonicsDunkl weight function

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Other transformations of harmonic type (42C20) Best constants in approximation theory (41A44)

Related Items (1)

A sharp Jackson inequality in \(L_p (\mathbb{R}^d)\) with Dunkl weight

Cites Work

• Direct and inverse theorems in approximation theory for periodic functions in S.B. Stechkin's papers and the development of these theorems
• Jung constants of the \(\ell ^ n_ p\)-spaces
• Jung's constant for the space \(L_ p\)
• Lower bound on constant in Jackson inequality in different \(L_ p\)- norms
• Reflection groups and orthogonal polynomials on the sphere
• Approximation of functions in the spaces \(L_ p\)
• On the relation between the Jackson and Jung constants of the spaces \(L_ p\)
• The sharp Jackson inequality in the space \(L_p\) on the sphere
• Approximation in \(L_ p\) by means of piecewise-constant functions
• Differential-Difference Operators Associated to Reflection Groups
• Integral Kernels with Reflection Group Invariance
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Orthogonal Polynomials of Several Variables
• Inequalities: theory of majorization and its applications
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