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

@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 < α < 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 < α < 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 -