Константы Никольского в пространствах $L^{p}(\mathbb{R},|x|^{2\alpha+1}\,dx)$

DOI10.22405/2226-8383-2018-19-2-67-79zbMath1434.41021OpenAlexW2913470251MaRDI QIDQ5109630

N. N. Dobrovol'skii, Dmitry Gorbachev

Publication date: 13 May 2020

Published in: Чебышевский сборник (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/cheb639

zbMATH Keywords

entire function of exponential typereproducing kernelBessel functionsharp constantgeneralized translation operatorDunkl transformweighted Nikolskii inequality

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Special classes of entire functions of one complex variable and growth estimates (30D15) Best constants in approximation theory (41A44)

Related Items (3)

Bounds of the Nikol'skii polynomial constants in \(L^p\) with Gegenbauer weight ⋮ Unnamed Item ⋮ Bernstein inequality in \(L^p\) on the line with power weight for \(p>0\)

Cites Work

• Nikol'skii type inequality; Bessel weight; extremal functions; extremal constants
• Inequality of different metrics for trigonometric polynomials
• Nikolskii constants for polynomials on the unit sphere
• Some problems of approximation theory in the spaces \(L_p\) on the line with power weight
• Positive \(L^p\)-bounded Dunkl-type generalized translation operator and its applications
• A weighted uniform $L^{p}$--estimate of Bessel functions: A note on a paper of Guo
• Bessel harmonic analysis and approximation of functions on the half-line
• Extremum problems for entire functions of exponential spherical type
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