Geodesic
Spline Wavelet Decomposition in Weighted Function Spaces
Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 313-337

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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.
Mots-clés : Besov space
Keywords: Triebel–Lizorkin space, local Muckenhoupt weight, Battle–Lemarié wavelet system, $B$-spline, decomposition theorem. 
@article{TRSPY_2021_312_a19,
     author = {E. P. Ushakova},
     title = {Spline {Wavelet} {Decomposition} in {Weighted} {Function} {Spaces}},
     journal = {Informatics and Automation},
     pages = {313--337},
     publisher = {mathdoc},
     volume = {312},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a19/}
}
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E. P. Ushakova. Spline Wavelet Decomposition in Weighted Function Spaces. Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 313-337. http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a19/