Boundedness and Compactness of Localization Operators Associated with the Spherical Mean Wigner Transform

Abstract

We introduce the notion of localization operators associated with the spherical mean Wigner transform, and we give a trace formula for the localization operators associated with the spherical mean Wigner transform as a bounded linear operator in the trace class from $$L^{2}(d\nu )$$ into $$L^{2}(d\nu )$$ in terms of the symbol and the two admissible wavelets. Next, we give results on the boundedness and compactness of localization operators associated with the spherical mean Wigner transform on $$L^{p}(d\nu )$$ , $$1 \le p \le \infty $$ .