E. P. Ushakova, “Spline Wavelet Decomposition in Weighted Function Spaces”, Trudy Mat. Inst. Steklova, 2021, Volume 312,Pages <nobr>313

This article is cited in 4 papers

Spline Wavelet Decomposition in Weighted Function Spaces

E. P. Ushakova^abc

^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

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.

UDC: 517.51

Received: May 22, 2020
Revised: September 1, 2020
Accepted: September 3, 2020

DOI: 10.4213/tm4132