Spline wavelet decomposition 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
Battle–Lemarié wavelet systems of natural orders are established in the paper. The main result of the work is decomposition theorem in Besov and Triebel–Lizorkin spaces with local Muckenhoupt weights, which is performed in terms of bases generated by the systems of such a type. Battle–Lemarié wavelets are splines and suit very well for the study of integration operators.
|Russian Science Foundation
|Far Eastern Branch of the Russian Academy of Sciences
|Russian Foundation for Basic Research
|The results of § 4 of the work were performed at Steklov Mathematical Institute of Russian Academy of Sciences under financial support of the Russian Science Foundation (project 19-11-00087). The work of the rest part of the paper was carried out within the framework of the State Tasks of Ministry of Education and Science of Russian Federation for V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences and Computing Center of Far–Eastern Branch of Russian Academy of Sciences, it was also partially supported by the Russian Foundation for Basic Research (project 19–01–00223).
Received: June 7, 2020
Revised: September 1, 2020
Accepted: September 3, 2020
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