Bounds of the Nikol'skii polynomial constants in \(L^p\) with Gegenbauer weight

DOI10.1134/S0081543821060109zbMath1494.41005OpenAlexW4205927651MaRDI QIDQ2071610

I. A. Mart'yanov, Dmitry Gorbachev

Publication date: 28 January 2022

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

Full work available at URL: https://doi.org/10.1134/s0081543821060109

zbMATH Keywords

asymptotic behaviorentire function of exponential typealgebraic polynomialsharp constanttrigonometric polynomialNikol'skii inequalityGegenbauer weight

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (1)

On constants in the Bernstein-Szegő inequality for the Weyl derivative of order less than unity of trigonometric polynomials and entire functions of exponential type in the uniform norm

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere
• Sharp constants in V. A. Markov-Bernstein type inequalities of different metrics
• Asymptotic behavior of Nikolskii constants for polynomials on the unit circle
• Nikol'skii inequality between the uniform norm and \(L_q\)-norm with ultraspherical weight of algebraic polynomials on an interval
• Polynomials of extremal \(L_p\)-norm on the \(L_\infty\)-unit sphere
• Nikol'skii type inequality; Bessel weight; extremal functions; extremal constants
• Estimates of the asymptotic Nikolskii constants for spherical polynomials
• Nikolskii constants for polynomials on the unit sphere
• Sharp constants of approximation theory. I. Multivariate Bernstein-Nikolskii type inequalities
• Sharp constants of approximation theory. III. Certain polynomial inequalities of different metrics on convex sets
• On sharp constants in Bernstein-Nikolskii inequalities
• Bernstein-Nikolskii inequalities and Riesz interpolation formula on compact homogeneous manifolds
• Positive \(L^p\)-bounded Dunkl-type generalized translation operator and its applications
• Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds
• Approximation Theory and Harmonic Analysis on Spheres and Balls
• Константы Никольского в пространствах $L^{p}(\mathbb{R},|x|^{2\alpha+1}\,dx)$
• О взаимосвязи констант Никольского для тригонометрических полиномов и целых функций экспоненциального типа

This page was built for publication: Bounds of the Nikol'skii polynomial constants in \(L^p\) with Gegenbauer weight