Localization Operators on Sobolev Spaces

Abstract

In this paper, we discuss some generalizations coming from wavelet transform on Sobolev spaces. In particular, we introduce the bounded localization operators on Sobolev spaces which are related to multi-dimensional wavelet transform on Sobolev spaces. Moreover, we propose the localization operators on Sobolev spaces are in $p$-Schatten class and they are compact. Finally, we give the boundedness and compactness of localization operators on Sobolev spaces with two admissible wavelets.