Sharp upper bounds of norms of functions and their derivatives on classes of functions with given comparison function

DOI10.1007/s11253-011-0567-zzbMath1231.41025OpenAlexW2079093430MaRDI QIDQ660687

V. A. Kofanov

Publication date: 4 February 2012

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

Full work available at URL: https://doi.org/10.1007/s11253-011-0567-z

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) Spline approximation (41A15) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (12)

Sharp Remez-type inequalities of various metrics in the classes of functions with given comparison function ⋮ Inequalities for derivatives of functions on an axis with nonsymmetrically bounded higher derivatives ⋮ Bojanov-Naidenov problem for differentiable functions and the Erdős problem for polynomials and splines ⋮ Sharp Kolmogorov-Remez-type inequalities for periodic functions of low smoothness ⋮ Sharp Remez-type inequalities of various metrics with asymmetric restrictions imposed on the functions ⋮ Sharp Remez-type inequalities for differentiable periodic functions, polynomials, and splines ⋮ Sharp Remez-type inequalities of different metrics for differentiable periodic functions, polynomials, and splines ⋮ Inequalities for nonperiodic splines on the real axis and their derivatives ⋮ The Bojanov-Naidenov problem for functions with asymmetric restrictions for the higher derivative ⋮ On the relationship between sharp Kolmogorov-type inequalities and sharp Kolmogorov-Remez-type inequalities ⋮ Bojanov-Naidenov problem for differentiable functions on the real line and the inequalities of various metrics ⋮ Sharp Remez-type inequalities estimating the \(L_q\)-norm of a function via its \(L_p\)-norm

Cites Work

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• Variations on the Chebyshev and \(L^ q\) theories of best approximation
• Inequalities for upper bounds of functionals
• Norm inequalities for derivatives and differences
• An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdős
• Investigations of dnepropetrovsk mathematicians related to inequalities for derivatives of periodic functions and their applications
• On some extremal problems of different metrics for differentiable functions on the axis
• Comparison of Exact Constants in Inequalities for Derivatives of Functions Defined on the Real Axis and a Circle

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