Some remarks on restriction of the Fourier transform for general measures

Autores: Fernando Soria de Diego , Per Sjölin
Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 43, Nº 2, 1999, págs. 655-664
Idioma: inglés
DOI: 10.5565/publmat_43299_07
Títulos paralelos:
- Algunas notas acerca de las restricciones de la transformada de Fourier para medidas generales
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Resumen
- 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 $0<\alpha<1$.