V. F. Babenko, S. A. Pichugov, “Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying Hölder Conditions”, Mat. Zametki, 87:1 (2010), 26–34; Math. Notes, 87:1 (2010), 23

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Matematicheskie Zametki, 2010, Volume 87, Issue 1, Pages 26–34
DOI: https://doi.org/10.4213/mzm5180 (Mi mzm5180)

This article is cited in 9 scientific papers (total in 9 papers)

Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying Hölder Conditions

V. F. Babenko^a, S. A. Pichugov^b

^a Dnepropetrovsk National University
^b Dnepropetrovsk National University of Railway Transport

Full-text PDF (464 kB) Citations (9)

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DOI: https://doi.org/10.4213/mzm5180

Abstract: We prove a new sharp Kolmogorov-type inequality that estimates the uniform norm of a mixed derivative of fractional order (in the sense of Marchaud) of a function of several variables via the uniform norm of the function and its norm on Hölder spaces.

Keywords: Marchaud fractional derivative, essentially bounded function, Kolmogorov-type inequality, Hölder condition, Hölder space.

Received: 05.06.2008
Revised: 26.05.2009

English version:
Mathematical Notes, 2010, Volume 87, Issue 1, Pages 23–30
DOI: https://doi.org/10.1134/S0001434610010049

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: V. F. Babenko, S. A. Pichugov, “Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying Hölder Conditions”, Mat. Zametki, 87:1 (2010), 26–34; Math. Notes, 87:1 (2010), 23–30

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm5180

https://doi.org/10.4213/mzm5180

https://www.mathnet.ru/eng/mzm/v87/i1/p26

This publication is cited in the following 9 articles:

Vladyslav Babenko, Oleg Kovalenko, Nataliia Parfinovych, “On approximation of hypersingular integral operators by bounded ones”, Journal of Mathematical Analysis and Applications, 513:2 (2022), 126215
M. Sh. Shabozov, M. O. Akobirshoev, “O neravenstvakh tipa Kolmogorova dlya periodicheskikh funktsii dvukh peremennykh v $L_2$ ”, Chebyshevskii sb., 20:2 (2019), 348–365
Nataliia V. Parfinovych, “Kolmogorov inequalities for the norms of the Riesz derivatives of functions of many variables”, J Math Sci, 229:1 (2018), 85
Babenko V.F. Parfinovich N.V., “Estimation of the Uniform Norm of One-Dimensional Riesz Potential of the Partial Derivative of a Function with Bounded Laplacian”, Ukr. Math. J., 68:7 (2016), 987–999
V. F. Babenko, N. V. Parfinovich, S. A. Pichugov, “Kolmogorov-Type Inequalities for Norms of Riesz Derivatives of Functions of Several Variables with Laplacian Bounded in $L_\infty$ and Related Problems”, Math. Notes, 95:1 (2014), 3–14
V. F. Babenko, M. S. Churilova, N. V. Parfinovych, D. S. Skorokhodov, “Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line”, J. Inequal. Appl., 2014, 504
Vladislav F. Babenko, Natal'ya V. Parfinovich, “Inequalities of the Kolmogorov type for norms of Riesz derivatives of multivariate functions and some of their applications”, J Math Sci, 187:1 (2012), 9
V. F. Babenko, N. V. Parfinovich, “Kolmogorov-type inequalities for the norms of Riesz derivatives of multivariable functions and some applications”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 9–20
Babenko V.F., Parfinovych N.V., Pichugov S.A., “Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions”, Ukrainian Math. J., 62:3 (2010), 343–357

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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