Some remarks on restriction of the Fourier tranform for general measures.

Sjölin, Per, and Soria, Fernando. "Some remarks on restriction of the Fourier tranform for general measures.." Publicacions Matemàtiques 43.2 (1999): 655-664. <http://eudml.org/doc/41379>.

@article{Sjölin1999,
abstract = {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 &lt; α &lt; 1.},
author = {Sjölin, Per, Soria, Fernando},
journal = {Publicacions Matemàtiques},
keywords = {Transformada de Fourier; Teoría de la medida; measure; Fourier transform; average decay; restriction theorem; Hausdorff dimension},
language = {eng},
number = {2},
pages = {655-664},
title = {Some remarks on restriction of the Fourier tranform for general measures.},
url = {http://eudml.org/doc/41379},
volume = {43},
year = {1999},
}

TY - JOUR
AU - Sjölin, Per
AU - Soria, Fernando
TI - Some remarks on restriction of the Fourier tranform for general measures.
JO - Publicacions Matemàtiques
PY - 1999
VL - 43
IS - 2
SP - 655
EP - 664
AB - 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 &lt; α &lt; 1.
LA - eng
KW - Transformada de Fourier; Teoría de la medida; measure; Fourier transform; average decay; restriction theorem; Hausdorff dimension
UR - http://eudml.org/doc/41379
ER -