Revistes Catalanes amb Accés Obert (RACO)

Some remarks on restriction of the Fourier transform for general measures

P. Sjölin, F. Soria


In this paper we 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. We also present a generalization of the classical restriction theorem of Stein and Tomas replacing the sphere with sets of prefixed Hausdorff dimension $n-1+\alpha$, with $0 < \alpha < 1$.

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