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 + α, with 0 < α < 1.
@article{urn:eudml:doc:41379,
title = {Some remarks on restriction of the Fourier tranform for general measures.},
journal = {Publicacions Matem\`atiques},
volume = {43},
year = {1999},
pages = {655-664},
mrnumber = {MR1744623},
zbl = {0958.42011},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41379}
}
Sjölin, Per; Soria, Fernando. Some remarks on restriction of the Fourier tranform for general measures.. Publicacions Matemàtiques, Tome 43 (1999) pp. 655-664. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41379/