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

• Hatem Mejjaoli
• Khalifa Trimèche
Article

## 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 $$L^{p}(d\nu )$$, $$1 \le p \le \infty$$.

## Keywords

Spherical mean operator Spherical mean Wigner transform Localisation operators

## Mathematics Subject Classification

33E30 42B10 43A32 44A20

## Notes

### Acknowledgements

The authors are deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article. The first author thanks the professor M.W. Wong for his help.

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