Generalized Jackson inequality in the space \(L_2(\mathbb{R}^{d})\) with Dunkl weight

DOI10.1134/S0081543815020108zbMath1332.46039MaRDI QIDQ2516598

Ha Thi Minh Hue, Valeriĭ I. Ivanov

Publication date: 3 August 2015

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

modulus of continuityJackson inequalityroot systembest approximationreflection groupDunkl transformDunkl weight

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

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Cites Work

• Dunkl's theory and Jackson's theorem in the space \(L_2(\mathbb R^d)\) with power weight
• Jackson inequality in \(L_{2}(\mathbb R^{N})\) with generalized modulus of continuity
• Jackson's theorem in the space \(L_{2}(\mathbb R^{d})\) with power weight
• Multidimensional Jackson theorem in \(L_ 2\).
• Optimal arguments in Jackson's inequality in the power-weighted space \(L_2(\mathbb R^d)\)
• A positive radial product formula for the Dunkl kernel
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