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Mat. Zametki, 2010, Volume 87, Issue 1, Pages 26–34 (Mi mz5180)  

This article is cited in 5 scientific papers (total in 5 papers)

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

V. F. Babenkoa, S. A. Pichugovb

a Dnepropetrovsk National University
b Dnepropetrovsk National University of Railway Transport

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

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

Full text: PDF file (464 kB)
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English version:
Mathematical Notes, 2010, 87:1, 23–30

Bibliographic databases:

UDC: 517.5
Received: 05.06.2008
Revised: 26.05.2009

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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    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. 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  crossref  mathscinet  zmath  isi  scopus
    2. 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  mathnet  crossref  isi  elib
    3. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    4. 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  crossref  mathscinet  zmath  isi  scopus
    5. 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  crossref  mathscinet  isi  scopus
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