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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2023 Volume 323, Pages 127–136 (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

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.

UDC: 517.51

Received: January 19, 2023
Revised: March 17, 2023
Accepted: July 17, 2023

DOI: 10.4213/tm4365


 English version: Proceedings of the Steklov Institute of Mathematics, 2023, 323, 120–129

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© Steklov Math. Inst. of RAS, 2025