Por Marco Fraccaroli (Basque Center for Applied Mathematics).

Forms associated with the superposition of bilinear Hilbert transforms appear in many contexts in analysis. For example, developing calculus for pseudo differential operators and studying Cauchy intergrals on Lipschitz curves.

In view of these applications, the question of uniform bounds for such bilinear Hilbert transforms arose. We will explore this problem with a special focus on the multidimensional case. In particular, we will describe the main tool in the time-frequency analysis of such operators, the phase plane projection. This projection concerns the appropriate simultaneous localization of both a function and its Fourier transform to specific regions of the time-frequency support.

This talk is based on joint work with Olli Saari, Christoph Thiele, and Gennady Uraltsev.

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.

Transmissão via Zoom (pw: lisbonwade).