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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 2, Pages 3–24 (Mi izv560)  

This article is cited in 4 scientific papers (total in 4 papers)

The modified multiplicative integral and derivative of arbitrary order on the semiaxis

S. S. Volosivets

Saratov State University named after N. G. Chernyshevsky

Abstract: We consider the modified strong dyadic integral and derivative in $L_q({\mathbb R}_+)$, $1\le q\le 2$. We establish conditions for their existence, study how the behaviour of the structural characteristics of a function is related to that of its derivative (integral), and prove an embedding theorem of Hardy–Littlewood–Sobolev type.

DOI: https://doi.org/10.4213/im560

Full text: PDF file (566 kB)
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English version:
Izvestiya: Mathematics, 2006, 70:2, 211–231

Bibliographic databases:

UDC: 517.2
MSC: 42C10, 26A33, 43A25
Received: 19.05.2005

Citation: S. S. Volosivets, “The modified multiplicative integral and derivative of arbitrary order on the semiaxis”, Izv. RAN. Ser. Mat., 70:2 (2006), 3–24; Izv. Math., 70:2 (2006), 211–231

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. S. Volosivets, “Hardy and Bellman transformations of series with respect to multiplicative systems”, Sb. Math., 199:8 (2008), 1111–1137  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. S. S. Volosivets, “The modified $\mathbf P$-integral and $\mathbf P$-derivative and their applications”, Sb. Math., 203:5 (2012), 613–644  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. S. S. Volosivets, “Modified Bessel ${\mathbf P}$-integrals and $\mathbf P$-derivatives and their properties”, Izv. Math., 78:5 (2014), 877–901  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. S. S. Volosivets, B. I. Golubov, “Uniform Convergence and Integrability of Multiplicative Fourier Transforms”, Math. Notes, 98:1 (2015), 53–67  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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