Geodesic
Measures with Fourier Transforms in L 2 of a Half-space
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 172-179

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DOI

We prove that if the Fourier transform of a compactly supported measure is in ${{L}^{2}}$ of a half-space, then the measure is absolutely continuous to Lebesgue measure. We then show how this result can be used to translate information about the dimensionality of a measure and the decay of its Fourier transform into geometric information about its support.
DOI : 10.4153/CMB-2010-077-2
Mots-clés : 42B10, 28A75 
Shayya, Bassam. Measures with Fourier Transforms in L 2 of a Half-space. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 172-179. doi: 10.4153/CMB-2010-077-2
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     doi = {10.4153/CMB-2010-077-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2010-077-2/}
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