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This paper addresses the sharpness of a weighted    L  2   ‐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    log  R   ‐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    .

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