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

DOI10.1134/S0001434619050031zbMath1429.41010OpenAlexW2953594099MaRDI QIDQ2334904

Dmitry Gorbachev, Valeriĭ I. Ivanov

Publication date: 8 November 2019

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434619050031

zbMATH Keywords

modulus of continuityJackson inequalitybest approximationgeneralized shift operatorDunkl transform

Mathematics Subject Classification ID

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

Related Items (2)

Sharp approximation theorems and Fourier inequalities in the Dunkl setting ⋮ Unnamed Item

Cites Work

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• On the sharpness of Jackson's inequality in the spaces \(L_p\) on the half-line with power weight
• Generalized Hermite polynomials and the heat equation for Dunkl operators
• Bohman extremal problem for the Dunkl transform
• Approximation of functions in the spaces \(L_ p\)
• On the constant in the Jackson inequality for the space \(L^ p(-\infty,+\infty)\)
• The sharp Jackson inequality in the space \(L_p\) on the sphere
• Optimal arguments in Jackson's inequality in the power-weighted space \(L_2(\mathbb R^d)\)
• Convolution operator and maximal function for the Dunkl transform
• Positive \(L^p\)-bounded Dunkl-type generalized translation operator and its applications
• A positive radial product formula for the Dunkl kernel
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Точное неравенство Джексона в $L_p(\mathbb R^d)$ с весом Данкля
• Bessel harmonic analysis and approximation of functions on the half-line
• Extremum problems for entire functions of exponential spherical type

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