Some remarks on restriction of the Fourier transform for general measures (Q1970330)

The authors establish a formal connection between the average decay of the Fourier transform of functions with respect to a given measure and the Hausdorff behavior of that measure. Their results are sharp for certain measures. The authors also give a generalization of the classical restriction theorem of Stein and Tomas replacing the sphere with sets of prefixed Hausdorff dimension \(n-1+\alpha\) with \(0<\alpha<1\).