Wavelet shrinkage estimators of Calderón-Zygmund operators with odd kernels

Abstract

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 Calderon-Zygmund operators T, it is interesting to construct estimator of Tf, 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 Tf is presented in this paper. The almost everywhere convergence and norm convergence of the proposed estimators are established.