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Mat. Sb., 1997, Volume 188, Number 12, Pages 73–106 (Mi msb274)  

This article is cited in 26 scientific papers (total in 27 papers)

Kolmogorov-type inequalities for derivatives

G. G. Magaril-Il'yaeva, V. M. Tikhomirovb

a Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University)
b M. V. Lomonosov Moscow State University

Abstract: The general problem of inequalities for derivatives consists in finding an estimate of some derivative of a function in terms of the norms of other derivatives. The aim of this paper is to overview problems of this kind from the general position of extremum theory.

DOI: https://doi.org/10.4213/sm274

Full text: PDF file (464 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 1997, 188:12, 1799–1832

Bibliographic databases:

UDC: 517.97
MSC: 26D10, 49J30
Received: 05.06.1997

Citation: G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Kolmogorov-type inequalities for derivatives”, Mat. Sb., 188:12 (1997), 73–106; Sb. Math., 188:12 (1997), 1799–1832

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Ilyin, “Best constants in a class of polymultiplicative inequalities for derivatives”, Sb. Math., 189:9 (1998), 1335–1359  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. V. Arestov, “The best approximation to a class of functions of several variables by another class and related extremum problems”, Math. Notes, 64:3 (1998), 279–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. M. I. Zelikin, L. F. Zelikina, “Exact Constants in Kolmogorov-Type Inequalities”, Proc. Steklov Inst. Math., 227 (1999), 131–139  mathnet  mathscinet  zmath
    4. Brinkhuis, J, “On a geometrical construction of the multiplier rule”, Indagationes Mathematicae-New Series, 11:4 (2000), 517  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. J. Brinkhuis, “On the Fermat–Lagrange principle for mixed smooth convex extremal problems”, Sb. Math., 192:5 (2001), 641–649  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of functions and their derivatives from Fourier coefficients prescribed with an error”, Sb. Math., 193:3 (2002), 387–407  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. M. I. Zelikin, “The Structure of Optimal Synthesis in the Vicinity of Singular Manifolds for Problems Affine with Respect to Control”, Proc. Steklov Inst. Math., 236 (2002), 164–185  mathnet  mathscinet  zmath
    8. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivatives”, Funct. Anal. Appl., 37:3 (2003), 203–214  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    9. V. I. Burenkov, V. A. Gusakov, “On Sharp Constants in Inequalities for the Modulus of a Derivative”, Proc. Steklov Inst. Math., 243 (2003), 98–119  mathnet  mathscinet  zmath
    10. G. G. Magaril-Il'yaev, K. Yu. Osipenko, V. M. Tikhomirov, “Indefinite Knowledge about an Object and Accuracy of Its Recovery Methods”, Problems Inform. Transmission, 39:1 (2003), 104–118  mathnet  crossref  mathscinet  zmath
    11. G. G. Magaril-Ilyaev, K. Yu. Osipenko, “Optimalnoe vosstanovlenie proizvodnykh na sobolevskikh klassakh”, Vladikavk. matem. zhurn., 5:1 (2003), 39–47  mathnet  mathscinet  zmath  elib
    12. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform”, Sb. Math., 195:10 (2004), 1461–1476  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. V. M. Tikhomirov, “Specific problems and general extremum theory”, Proc. Steklov Inst. Math. (Suppl.), 2004no. , suppl. 2, S154–S167  mathnet  mathscinet  zmath  elib
    14. S. S. Chudova, “Optimalnoe vosstanovlenie integrala po $D$-mernomu sharu”, Vladikavk. matem. zhurn., 6:4 (2004), 63–67  mathnet  mathscinet  zmath  elib
    15. J. Mashreghi, F. L. Nazarov, V. P. Havin, “Beurling–Malliavin multiplier theorem: the seventh proof”, St. Petersburg Math. J., 17:5 (2006), 699–744  mathnet  crossref  mathscinet  zmath  elib
    16. G. G. Magaril-Ilyaev, “Pyat syuzhetov o tvorchestve Vladimira Mikhailovicha Tikhomirova”, Matem. prosv., ser. 3, 10, Izd-vo MTsNMO, M., 2006, 8–22  mathnet
    17. K. Yu. Osipenko, “The Hardy–Littlewood–Pólya inequality for analytic functions in Hardy–Sobolev spaces”, Sb. Math., 197:3 (2006), 315–334  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On the reconstruction of convolution-type operators from inaccurate information”, Proc. Steklov Inst. Math., 269 (2010), 174–185  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    20. G. G. Magaril-Il'yaev, E. O. Sivkova, “Best recovery of the Laplace operator of a function from incomplete spectral data”, Sb. Math., 203:4 (2012), 569–580  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. E. O. Sivkova, “Ob optimalnom vosstanovlenii laplasiana funktsii po ee netochno zadannomu preobrazovaniyu Fure”, Vladikavk. matem. zhurn., 14:4 (2012), 63–72  mathnet
    22. Aliev A.R., Mohamed A.S., “On the Well-Posedness of a Boundary Value Problem for a Class of Fourth-Order Operator-Differential Equations”, Differ. Equ., 48:4 (2012), 596–598  crossref  mathscinet  zmath  isi  elib  scopus
    23. E. O. Sivkova, “Best recovery of the Laplace operator of a function and sharp inequalities”, J. Math. Sci., 209:1 (2015), 130–137  mathnet  crossref  mathscinet
    24. S. V. Zelik, A. A. Ilyin, “Green's function asymptotics and sharp interpolation inequalities”, Russian Math. Surveys, 69:2 (2014), 209–260  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    25. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Exactness and optimality of methods for recovering functions from their spectrum”, Proc. Steklov Inst. Math., 293 (2016), 194–208  mathnet  crossref  crossref  mathscinet  isi  elib
    26. A. S. Kochurov, “Inequalities between the norms of a function and its derivatives”, Eurasian Math. J., 7:1 (2016), 28–49  mathnet
    27. Aliev A.R. Mirzoev S.S. Soylemezo M.A., “on Solvability of Third-Order Operator Differential Equation With Parabolic Principal Part in Weighted Space”, J. Funct. space, 2017, 2932134  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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