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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 6, Pages 1382–1410
DOI: https://doi.org/10.33048/smzh.2022.63.616 (Mi smj7738) 		 
This article is cited in 3 scientific papers (total in 3 papers)

The images of integration operators in weighted function spaces

E. P. Ushakovaabc

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c Computer Centre of Far Eastern Branch RAS, Khabarovsk
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DOI: https://doi.org/10.33048/smzh.2022.63.616
Abstract: We obtain conditions for the validity of norm inequalities on the images and preimages of integration operators of positive integer orders in the Besov and Triebel–Lizorkin spaces with local Muckenhoupt weights on ${\Bbb R}^N$. As application, we establish a connection between the entropy and approximative numbers of the embedding operators and the same characteristics of the integration operators.
Keywords: Riemann–Liouville operator, Besov and Triebel–Lizorkin spaces, local Muckenhoupt weight, Battle–Lemarié spline-type wavelet system, atomic decomposition.
Funding agency Grant number
Russian Science Foundation 22-21-00579
19-11-00087
Ministry of Science and Higher Education of the Russian Federation
The research in Section 5 was supported by the Russian Science Foundation (Grant no. 22–21–00579; https:// rscf.ru/project/22–21–00579/). The results of Sections 4 and 6 were obtained at the Steklov Institute of Mathematics and supported by Grant no. 19–11–00087 (https://rscf.ru/project/19–11–00087/). The rest of the article was carried out in the framework of the State Task with the Ministry of Science and Higher Education of the Russian Federation to the Trapeznikov Institute of Control Sciences and the Computing Center of the Far Eastern Branch of the Russian Academy of Sciences.
Received: 05.02.2022
Revised: 05.02.2022
Accepted: 15.08.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 6, Pages 1181–1207
DOI: https://doi.org/10.1134/S0037446622060167
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: 35R30
Language: Russian
Citation: E. P. Ushakova, “The images of integration operators in weighted function spaces”, Sibirsk. Mat. Zh., 63:6 (2022), 1382–1410; Siberian Math. J., 63:6 (2022), 1181–1207
Citation in format AMSBIB
\Bibitem{Ush22}
\by E.~P.~Ushakova
\paper The images of integration operators in weighted function spaces
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 6
\pages 1382--1410
\mathnet{http://mi.mathnet.ru/smj7738}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4528757}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 6
\pages 1181--1207
\crossref{https://doi.org/10.1134/S0037446622060167}
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