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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2023, Volume 323, Pages 127–136
DOI: https://doi.org/10.4213/tm4365 (Mi tm4365) 		 
Riemann–Liouville Space of Fractional Potentials on the Half-Line

M. L. Goldmana, V. D. Stepanovba

a Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680000 Russia
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DOI: https://doi.org/10.4213/tm4365
Abstract: We study the Riemann–Liouville space of fractional potentials on the half-line and establish its properties such as embeddings in Besov spaces, Liouville classes, and Lizorkin–Triebel spaces.
Keywords: Riemann–Liouville fractional integral, embedding, Besov space, Lizorkin–Triebel space.
Funding agency Grant number
Russian Science Foundation 19-11-00087
Ministry of Science and Higher Education of the Russian Federation
The work presented in Sections 1 and 2 was supported by the Russian Science Foundation under grant no. 19-11-00087, https://rscf.ru/en/project/19-11-00087/, and performed at the Steklov Mathematical Institute of Russian Academy of Sciences. The rest of the study was carried out within the state task of the Ministry of Science and Higher Education of the Russian Federation for the Computing Center of the Far Eastern Branch of the Russian Academy of Sciences.
Received: January 19, 2023
Revised: March 17, 2023
Accepted: July 17, 2023
English version:
Proceedings of the Steklov Institute of Mathematics, 2023, Volume 323, Pages 120–129
DOI: https://doi.org/10.1134/S0081543823050073
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: M. L. Goldman, V. D. Stepanov, “Riemann–Liouville Space of Fractional Potentials on the Half-Line”, Theory of Functions of Several Real Variables and Its Applications, Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday, Trudy Mat. Inst. Steklova, 323, Steklov Mathematical Institute of RAS, Moscow, 2023, 127–136; Proc. Steklov Inst. Math., 323 (2023), 120–129
Citation in format AMSBIB
\Bibitem{GolSte23}
\by M.~L.~Goldman, V.~D.~Stepanov
\paper Riemann--Liouville Space of Fractional Potentials on the Half-Line
\inbook Theory of Functions of Several Real Variables and Its Applications
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov on the occasion of his 90th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2023
\vol 323
\pages 127--136
\publ Steklov Mathematical Institute of RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4365}
\crossref{https://doi.org/10.4213/tm4365}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2023
\vol 323
\pages 120--129
\crossref{https://doi.org/10.1134/S0081543823050073}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85186933736}
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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