Spline wavelet decomposition in weighted function spaces

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.

Funding Agency	Grant Number
Russian Science Foundation	19-11-00087
Far Eastern Branch of the Russian Academy of Sciences
Russian Foundation for Basic Research	19-01-00223
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).