Weyl transforms associated with the Heisenberg group (Q2468518)

The authors define the Wigner transform and the corresponding Weyl transform associated with the Heisenberg group, and study some of their properties. Some results on harmonic analysis are established. The Weyl transform with \(S_p\)-valued symbol in \(L_p\) is not only bounded but also compact for \(p\in[1; 2]\). The proof is based on the Riesz-Thorin interpolation theorem, too. When \(p> 2\) the Weyl transform is an unbounded operator.