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

Volume 10, Issue 12, pp 6149--6158
Publication Date: December 02, 2017 Submission Date: September 20, 2017
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### 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].

### Share and Cite

##### ISRP Style

Junjian Zhao, Zhitao Zhuang, Wavelet thresholding estimator on $B_{p,q}^s(\mathbb{R}^n)$, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 12, 6149--6158

##### AMA Style

Zhao Junjian, Zhuang Zhitao, Wavelet thresholding estimator on $B_{p,q}^s(\mathbb{R}^n)$. J. Nonlinear Sci. Appl. (2017); 10(12):6149--6158

##### Chicago/Turabian Style

Zhao, Junjian, Zhuang, Zhitao. "Wavelet thresholding estimator on $B_{p,q}^s(\mathbb{R}^n)$." Journal of Nonlinear Sciences and Applications, 10, no. 12 (2017): 6149--6158

### Keywords

• Wavelet thresholding estimator
• Besov spaces
• convergence

•  42C40
•  35Q30
•  41A15

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