Short-time Fourier transform analysis of localization operators

We perform a detailed study of the boundedness properties for localization operators. The language and the tools employed are provided by time-frequency analysis. In particular, the time-frequency representation named short-time Fourier transform (STFT) is used both to define and to obtain the boundedness properties of localization operators. Our results widen most part of the ones known in the literature. Moreover, the sufficient conditions are worked out by STFT estimates, rather than the Weyl connections as done, e.g., in [4, 8]. Besides, the necessary boundedness conditions are referred to a fixed choice of window functions, so that we can claim the optimality of our results. Finally, we deal with the problem of finding symbol conditions for Weyl operators that guarantee to rewrite them as localization operators.