Sharp inequalities between the best root-mean-square approximations of analytic functions in the disk and some smoothness characteristics in the Bergman space

DOI10.1134/S0001434621070269zbMath1477.41006OpenAlexW3194648214WikidataQ114075410 ScholiaQ114075410MaRDI QIDQ2049309

N. U. Kadamshoev, Mirgand Shabozovich Shabozov

Publication date: 25 August 2021

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

Full work available at URL: https://doi.org/10.1134/s0001434621070269

zbMATH Keywords

sharp inequalities\(n\)-widthssmoothness characteristicsexact constantsbest joint approximation

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Rate of convergence, degree of approximation (41A25)

Cites Work

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• Inequalities between best polynomial approximations and some smoothness characteristics in the space \(L_2\) and widths of classes of functions
• Jackson's theorem in the space \(L^p(R^k),\;0<p<1\)
• The geometry of maximum principle
• Upper bounds for the approximation of certain classes of functions of a complex variable by Fourier series in the space \(L_2\) and \(n\)-widths
• Precise constant in Jackson's inequality for continuous periodic functions
• Direct and converse theorems of the theory of approximation in the metric of \(L_p\) for \(0<p<1\)
• Exact constants of approximation for differentiable periodic functions
• Best polynomial approximations in \(L_{2}\) of classes of \(2{\pi}\)-periodic functions and exact values of their widths
• Best approximation of periodic functions by trigonometric polinomials in \(L_ 2\)
• Jackson's theorem in \(L_{p}\)
• Sharp estimates for the convergence rate of Fourier series of complex variable functions in L 2(D, p(z))
• DIRECT AND CONVERSE THEOREMS OF JACKSON TYPE IN $ L^p$ SPACES, $ 0<p<1$
• Mean-square approximation of complex variable functions by Fourier series in the weighted Bergman space

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