A comparison of trilinear testing conditions for the paraboloid Fourier extension and Kakeya conjectures in three dimensions

We compare the smooth Alpert testing condition for the paraboloid Fourier extension conjecture in <cite>RiSa3</cite> to the modulated testing condition for the Kakeya conjecture in <cite>RiSa2</cite>. To this end, the modulated testing condition is converted to a certain restricted smooth Alpert testing condition for the paraboloid Fourier extension conjecture.