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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 6, Pages 25–34 (Mi ivm7501)  
This article is cited in 4 scientific papers (total in 4 papers)

Zygmund-type estimates for fractional integration and differentiation operators of variable order

B. G. Vakulova, E. S. Kochurova, N. G. Samkob

a Chair of Differential and Integral Equations, Southern Federal University, Rostov-on-Don, Russia
b Center of Functional Analysis and Applications, University of Algarve, Faro, Portugal
Full-text PDF (216 kB) Citations (4)
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Abstract: We consider non-standard generalized Hölder spaces of functions defined on a segment of the real axis, whose local continuity modulus has a majorant varying from point to point. We establish some properties of fractional integration operators of variable order acting from variable generalized Hölder spaces to those with a “better” majorant, as well as properties of fractional differentiation operators of variable order acting from the same spaces to those with a “worse” majorant.
Keywords: fractional integration operators, fractional differentiation operators, generalized continuity modulus, generalized Hölder spaces.
Received: 30.12.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 6, Pages 20–28
DOI: https://doi.org/10.3103/S1066369X11060041
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: B. G. Vakulov, E. S. Kochurov, N. G. Samko, “Zygmund-type estimates for fractional integration and differentiation operators of variable order”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 6, 25–34; Russian Math. (Iz. VUZ), 55:6 (2011), 20–28
Citation in format AMSBIB
\Bibitem{VakKocSam11}
\by B.~G.~Vakulov, E.~S.~Kochurov, N.~G.~Samko
\paper Zygmund-type estimates for fractional integration and differentiation operators of variable order
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 6
\pages 25--34
\mathnet{http://mi.mathnet.ru/ivm7501}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2931702}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 6
\pages 20--28
\crossref{https://doi.org/10.3103/S1066369X11060041}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051653667}
Linking options:
  • https://www.mathnet.ru/eng/ivm7501
  • https://www.mathnet.ru/eng/ivm/y2011/i6/p25
    • This publication is cited in the following 4 articles:
    1. Yuri E. Drobotov, Boris G. Vakulov, “HYPERSINGULAR INTEGRALS IN POWER-WEIGHTED VARIABLE GENERALIZED HÖLDER SPACES OVER METRIC MEASURE SPACES”, J Math Sci, 2024  crossref
    2. B. G. Vakulov, Yu. E. Drobotov, “Riesz Potential with Integrable Density in Hölder-Variable Spaces”, Math. Notes, 108:5 (2020), 652–660  mathnet  crossref  crossref  mathscinet  isi  elib
    3. B. G. Vakulov, Yu. E. Drobotov, “Operator tipa potentsiala peremennogo poryadka po $\mathbb{\dot{R}}^n$ v vesovykh prostranstvakh obobschennoi peremennoi gelderovosti”, Sib. elektron. matem. izv., 14 (2017), 647–656  mathnet  crossref
    4. Abreu-Blaya R., Bory-Reyes J., “The Plemelj-Privalov Theorem in Variable Exponent Clifford Analysis”, Georgian Math. J., 19:3 (2012), 401–415  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    Full-text PDF :103
    References:78
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