Some remarks on restriction of the Fourier tranform for general measures.
Per Sjölin, Fernando Soria (1999)
Publicacions Matemàtiques
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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 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 + α, with 0 < α < 1.