Caltech/UCLA Joint Analysis Seminar

The problem of restricting the Fourier transform of a non-integrable function to a hypersurface gained attention in the 1970s and is an active research field today. On the other hand, maximal Fourier restriction estimates were inaugurated recently by Müller, Ricci, and Wright in order to give a pointwise meaning to the restriction of the Fourier transform of a function. We will discuss variational Fourier restriction estimates, which quantify the pointwise convergence in question. Moreover, we will sketch a simple abstract argument that deduces certain maximal and variational Fourier restriction estimates from ordinary a priori estimates.