Restriction Conjecture Research Articles

Adjoint restriction estimates and scaling on spheres

We test the restriction conjecture, in its adjoint form, against a class of measures Φδdσ on the sphere S n-1 . The densities Φδ are smoothed out characteristic functions of δ a 2 x δ a 3 × ... × δ a n rectangular caps on S n-1 , where a 2 , a 3 ,...,a n are fixed nonnegative numbers.