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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 312, Pages 313–337
DOI: https://doi.org/10.4213/tm4132 (Mi tm4132) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Spline Wavelet Decomposition in Weighted Function Spaces

E. P. Ushakovaabc

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, ul. Profsoyuznaya 65, Moscow, 117997 Russia
b Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
c Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, ul. Kim Yu Chena 65, Khabarovsk, 680000 Russia
Full-text PDF (356 kB) Citations (4)
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DOI: https://doi.org/10.4213/tm4132
Abstract: We present Battle–Lemarié wavelet systems of natural orders. Our main result is a decomposition theorem in Besov and Triebel–Lizorkin spaces with local Muckenhoupt weights, which is formulated in terms of bases generated by systems of such a type. The Battle–Lemarié wavelets are splines and suit very well the study of integration operators.
Keywords: Besov space, Triebel–Lizorkin space, local Muckenhoupt weight, Battle–Lemarié wavelet system, B-spline, decomposition theorem.
Funding agency Grant number
Russian Science Foundation 19-11-00087
Ministry of Science and Higher Education of the Russian Federation
Russian Foundation for Basic Research 19-01-00223
The work presented in Section 4 is supported by the Russian Science Foundation under grant 19-11-00087 and performed in Steklov Mathematical Institute of Russian Academy of Sciences. The work presented in the other sections was carried out within the framework of the state tasks of the Ministry of Science and Higher Education of the Russian Federation for the V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences and for the Computing Center of the Far Eastern Branch of the Russian Academy of Sciences, and was also supported in part by the Russian Foundation for Basic Research (project no. 19-01-00223).
Received: May 22, 2020
Revised: September 1, 2020
Accepted: September 3, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 312, Pages 301–324
DOI: https://doi.org/10.1134/S008154382101020X
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: E. P. Ushakova, “Spline Wavelet Decomposition in Weighted Function Spaces”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 313–337; Proc. Steklov Inst. Math., 312 (2021), 301–324
Citation in format AMSBIB
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\by E.~P.~Ushakova
\paper Spline Wavelet Decomposition in Weighted Function Spaces
\inbook Function Spaces, Approximation Theory, and Related Problems of Analysis
\bookinfo Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 312
\pages 313--337
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4132}
\crossref{https://doi.org/10.4213/tm4132}
\elib{https://elibrary.ru/item.asp?id=46739372}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 312
\pages 301--324
\crossref{https://doi.org/10.1134/S008154382101020X}
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    • This publication is cited in the following 4 articles:
    1. Elena P. Ushakova, “THE STUDY BY SPLINES OF NORM INEQUALITIES FOR RIEMANN–LIOUVILLE OPERATORS IN WEIGHTED BESOV SPACES”, J Math Sci, 2024  crossref
    2. E. P. Ushakova, “Boundedness of the Hilbert transform in Besov spaces”, Anal. Math., 49:4 (2023), 1137–1174  mathnet  crossref  mathscinet
    3. E. P. Ushakova, K. E. Ushakova, “Norm inequalities with fractional integrals”, St. Petersburg Math. J., 35:3 (2024), 571–595  mathnet  crossref  isi
    4. E. P. Ushakova, “The images of integration operators in weighted function spaces”, Siberian Math. J., 63:6 (2022), 1181–1207  mathnet  crossref  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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