Localization Operators on Sobolev Spaces

In this paper, we discuss some generalizations coming from wavelet transform on sobolev spaces. in particular, we intro-duce 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 localiza-tion operators on sobolev spaces with two admissible wavelets.