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 / Description of output

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

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MULTIPLIERS

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10.1007/s11854-008-0004-x

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T1 - Localisation and weighted inequalities for spherical Fourier means

AU - Carbery, Anthony

AU - Soria, Fernando

AU - Vargas, Ana

PY - 2007/12

Y1 - 2007/12

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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.

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U2 - 10.1007/s11854-008-0004-x

DO - 10.1007/s11854-008-0004-x

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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

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