On Ahlfors–David regular weighted bounds for the extension operator associated to the circle

orponen, tuomas;

This paper addresses the sharpness of a weighted L2-estimate for the Fourier extension operator associated to the circle, obtained by J. Bennett, A. Carbery, F. Soria and A. Vargas in 2006. A point left open in their paper was the necessity of a certain logR-factor in the bound. Here, I show that the factor is necessary for all 1/2 -Ahlfors–David regular weights on the circle, but it can be removed for s-Ahlfors–David regular weights with s = 1/2 .