Joint BCAM-UPV/EHU Analysis and PDE seminar: The Fourier Extension problem through a new perspective

Abstract
An equivalent formulation of the Fourier Extension (F.E.) conjecture for a compact piece of the paraboloid states that the F.E. operator maps L2+ 2/𝑑 ([0,1]d) to L2+ 2/𝑑+𝜀(ℝ"d+1") for every ε > 0. It has been fully solved only for d = 1 and there are many partial results in higher dimensions regarding the range of (p, q) for which Lp([0, 1]d) is mapped to Lq(ℝd+1).
In this talk, we will take an alternative route to this problem: one can reduce matters to proving that a model operator satisfies the same mapping properties, and we will show that the conjecture holds in higher dimensions for tensor functions, meaning for all g of the form 
g(x1, . . . , xd) = g1(x1). . .gd(xd). Time permitting, we will also address multilinear versions of the statement above and get similar results, in which we will need only one of the many functions involved in each problem to be of such kind to obtain the desired conjectured bounds.
This is joint work with Camil Muscalu.

The results of this talk are joint work with R. G. Durán


Link to the session:
https://us06web.zoom.us/j/99649860282?pwd=SE0vemtYMFlwbFBNTXQyOTBONG0vZz09

More info at https://sites.google.com/view/apdebilbao/home