Spline wavelet decomposition in weighted function spaces
Elena P. Ushakova
TL;DR
This paper develops a decomposition theorem for Besov and Triebel-Lizorkin spaces with local Muckenhoupt weights using Battle-Lemarie spline wavelet bases, enhancing analysis in weighted function spaces.
Contribution
It introduces a new decomposition theorem in weighted Besov and Triebel-Lizorkin spaces using Battle-Lemarie wavelet systems, which are spline-based and suitable for studying integration operators.
Findings
Established Battle-Lemarie wavelet systems of natural orders.
Proved decomposition theorem in weighted Besov and Triebel-Lizorkin spaces.
Demonstrated suitability of spline wavelets for analyzing integration operators.
Abstract
Battle-Lemarie 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-Lemarie wavelets are splines and suit very well for the study of integration operators.
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