Continuità degli Operatori Pseudo-differenziali negli Spazi di Modulazione

The thesis is devoted to the study of the boundedness properties for pseudodifferential operators on modulation spaces. It is divided into two parts. The first part contains the basic aspects of time-frequency analysis. Namely, the fundamental operators and function spaces involved, such as the Short-time Fourier transform, the Wigner distribution, the modulation and Wiener amalgam spaces. The second part is the core of the thesis. It focus on the theory of pseudodifferential operators, which can be written in Kohn-Nirenberg or Weyl form. It contains boundedness result for pseudodifferential operator acting on modulation spaces, whose symbols first belong to Sjöstrand's class and next to general modulation spaces. Finally, new result in terms of sufficient conditions for the boundedness of Weyl operators on modulation spaces is introduced. In this case the Weyl symbols belong to the Wiener amalgam spaces. This is the first result which relates symbols in Wiener amalgam spaces to operators acting on modulation spaces.