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Algebra i Analiz, 2023, Volume 35, Issue 3, Pages 185–219 (Mi aa1871)  
This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

Norm inequalities with fractional integrals

E. P. Ushakovaab, K. E. Ushakovac

a Institute of Control Sciences
b Steklov Mathematical Institute of Russian Academy of Sciences
c Computer Centre of Far Eastern Branch RAS
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Abstract: Fractional spline wavelet systems are considered in the paper. With their help, as well as with the involvement of Battle–Lemarié scaling and wavelet functions of natural orders, conditions are found for the fulfillment of inequalities connecting norms of images and pre-images of fractional integration operators in Besov spaces with Muckenhupt weights on $\mathbb{R}$.
Keywords: Riemann-Liouville operator, Besov space, Muckenhoupt weight, spline wavelet basis, atomic decomposition, molecular representation.
Funding agency Grant number
Russian Science Foundation 19-11-00087
22-21-00579
Received: 20.02.2022
English version:
St. Petersburg Mathematical Journal, 2024, Volume 35, Issue 3, Pages 571–595
DOI: https://doi.org/10.1090/spmj/1817
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. P. Ushakova, K. E. Ushakova, “Norm inequalities with fractional integrals”, Algebra i Analiz, 35:3 (2023), 185–219; St. Petersburg Math. J., 35:3 (2024), 571–595
Citation in format AMSBIB
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\by E.~P.~Ushakova, K.~E.~Ushakova
\paper Norm inequalities with fractional integrals
\jour Algebra i Analiz
\yr 2023
\vol 35
\issue 3
\pages 185--219
\mathnet{http://mi.mathnet.ru/aa1871}
\transl
\jour St. Petersburg Math. J.
\yr 2024
\vol 35
\issue 3
\pages 571--595
\crossref{https://doi.org/10.1090/spmj/1817}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=001280525400001}
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  • https://www.mathnet.ru/eng/aa/v35/i3/p185
    • This publication is cited in the following 1 articles:
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