Note on the Wigner distribution and Localization Operators in the quasi-Banach setting

Time-frequency analysis have played a crucial role in the development of localization operators in the last 20 years. We present its applications to the study of boundedness and Schatten Class property for such operators. In particular, new sufficient conditions for such operators to belong to the Schatten-von Neumann Class \(S_p(L^2(\mathbb {R}^d))\), 0 < p < 1, are exhibited. As a byproduct, sharp continuity results for the Wigner distribution are also presented.