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

Loading [MathJax]/jax/output/CommonHTML/jax.js

Matematicheskie Zametki

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Zametki:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

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)

References:

PDF

HTML

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

\Bibitem{BabPic10}

\by V.~F.~Babenko, S.~A.~Pichugov

\paper Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying H\"older Conditions

\jour Mat. Zametki

\yr 2010

\vol 87

\issue 1

\pages 26--34

\mathnet{http://mi.mathnet.ru/mzm5180}

\crossref{https://doi.org/10.4213/mzm5180}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2730380}

\zmath{https://zbmath.org/?q=an:05791016}

\transl

\jour Math. Notes

\yr 2010

\vol 87

\issue 1

\pages 23--30

\crossref{https://doi.org/10.1134/S0001434610010049}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000276064800004}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77950015718}

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

Statistics & downloads:
Abstract page:	769
Full-text PDF :	275
References:	81
First page:	28

Registration to the website

Logotypes