Wavelet shrinkage estimators of Calderón-Zygmund operators with odd kernels  

作　　者：CHEN Heng WU JiTao 

机构地区：[1]Department of Mathematics,Beijing University of Aeronautics and Astronautics

出　　处：《Science China Mathematics》2014年第9期1983-1991,共9页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11171014 and 91130009);National Basic Research Program of China(Grant No.973-2010CB-731900)

摘　　要：Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression,signal processing and statistics,etc.For Calder′on-Zygmund operators T,it is interesting to construct estimator of T f,based on wavelet shrinkage estimator of f.With the help of a representation of operators on wavelets,due to Beylkin et al.,an estimator of T f is presented in this paper.The almost everywhere convergence and norm convergence of the proposed estimators are established.Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression,signal processing and statistics,etc.For Calder′on-Zygmund operators T,it is interesting to construct estimator of T f,based on wavelet shrinkage estimator of f.With the help of a representation of operators on wavelets,due to Beylkin et al.,an estimator of T f is presented in this paper.The almost everywhere convergence and norm convergence of the proposed estimators are established.

关 键 词：wavelets shrinkage singular integral operator non-standard form maximal operator 

分 类 号：O174.2[理学—数学]