On the boundedness of the Weyl transform for homogeneous distributions on $${\mathbb {R}}^2$$

Abstract

AbstractStarting from earlier work by M.W. Wong, we give necessary and sufficient criteria, respectively, for the boundedness of the Weyl transform $$W_\sigma $$Wσ as an operator on $$L^2({\mathbb {R}})$$L2(R) if $$\sigma $$σ is a homogeneous distribution on $${\mathbb {R}}^2$$R2.