Abstract
We introduce the notion of localization operators associated with the Riemann-Liouville-Wigner transform, and we give a trace formula for the localization operators associated with the Riemann-Liouville-Wigner transform as a bounded linear operator in the trace class from L-2 (d nu(alpha)) into L-2 (d nu(alpha)) 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 Riemann-Liouville-Wigner transform on L-p (d nu(alpha)), 1 <= p <= infinity.