Kolmogorov type inequalities for norms of Riesz derivatives of multivariate functions and some applications

DOI10.1134/S0081543812050033zbMath1304.41008MaRDI QIDQ742268

Vladislav F. Babenko, Nataliia Viktorivna Parfinovych

Publication date: 18 September 2014

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

zbMATH Keywords

fractional derivativeKolmogorov type inequalitiesapproximation of operators

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by operators (in particular, by integral operators) (41A35) Approximation by positive operators (41A36)

Related Items (6)

On a general approach to some problems of approximation of operators ⋮ Kolmogorov inequalities for the norms of the Riesz derivatives of functions of many variables ⋮ Estimation of the uniform norm of one-dimensional Riesz potential of the partial derivative of a function with bounded Laplacian ⋮ Kolmogorov-type inequalities for the norms of fractional derivatives of functions defined on the positive half line ⋮ Kolmogorov-type inequalities for norms of Riesz derivatives of functions of several variables with Laplacian bounded in \(L_\infty\) and related problems ⋮ Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line

Cites Work

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• On the Kolmogorov inequality for fractional derivatives on the half-line
• Norm inequalities for derivatives and differences
• Sharp estimates of the norms of fractional derivatives of functions of several variables satisfying Hölder conditions
• Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic
• Approximation of unbounded operators by bounded operators and related extremal problems

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