Wavelet thresholding estimator on \(B_{p,q}^s(\mathbb{R}^n)\)

Volume 10, Issue 12, pp 6149--6158

Publication Date: 2017-12-02

http://dx.doi.org/10.22436/jnsa.010.12.02

Authors

Junjian Zhao - Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin 300387, China
Zhitao Zhuang - School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Abstract

This paper deals with the convergence of the wavelet thresholding estimator on Besov spaces \(B_{p,q}^s(\mathbb{R}^n)\). We show firstly the equivalence of several Besov norms. It seems different with one dimensional case. Then we provide two convergence theorems for the wavelet thresholding estimator, which extend Liu and Wang's work [Y.-M. Liu, H.-Y. Wang, Appl. Comput. Harmon. Anal., \({\bf 32}\) (2012), 342--356].

Keywords

Wavelet thresholding estimator, Besov spaces, convergence

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