Localisation and weighted inequalities for spherical Fourier means

Anthony Carbery; Fernando Soria; Ana Vargas

doi:10.1007/s11854-008-0004-x

Localisation and weighted inequalities for spherical Fourier means

Anthony Carbery, Fernando Soria, Ana Vargas

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L-2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.

Original language	English
Pages (from-to)	133-156
Number of pages	24
Journal	Journal d'Analyse Mathématique
Volume	103
DOIs	https://doi.org/10.1007/s11854-008-0004-x
Publication status	Published - Dec 2007

Keywords / Materials (for Non-textual outputs)

MULTIPLIERS

Access to Document

10.1007/s11854-008-0004-x

Cite this

@article{2d0ad58b95be4fe3a6c4ac87365a322c,

title = "Localisation and weighted inequalities for spherical Fourier means",

abstract = "In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L-2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.",

keywords = "MULTIPLIERS",

author = "Anthony Carbery and Fernando Soria and Ana Vargas",

year = "2007",

month = dec,

doi = "10.1007/s11854-008-0004-x",

language = "English",

volume = "103",

pages = "133--156",

journal = "Journal d'Analyse Math{\'e}matique",

issn = "0021-7670",

publisher = "Springer",

}

TY - JOUR

T1 - Localisation and weighted inequalities for spherical Fourier means

AU - Carbery, Anthony

AU - Soria, Fernando

AU - Vargas, Ana

PY - 2007/12

Y1 - 2007/12

N2 - In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L-2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.

AB - In this work, we establish certain equivalences between the localisation properties with respect to spherical Fourier means of the support of a given Borel measure and the L-2-rate of decay of the Fourier extension operator associated to it. This, in turn, is intimately connected with the property that the X-ray transform of the measure be uniformly bounded. Geometric properties of sets supporting such a measure are studied.

KW - MULTIPLIERS

U2 - 10.1007/s11854-008-0004-x

DO - 10.1007/s11854-008-0004-x

M3 - Article

SN - 0021-7670

VL - 103

SP - 133

EP - 156

JO - Journal d'Analyse Mathématique

JF - Journal d'Analyse Mathématique

ER -

Localisation and weighted inequalities for spherical Fourier means

Abstract

Keywords / Materials (for Non-textual outputs)

Access to Document

Fingerprint

Cite this