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# Measures with Fourier Transforms in $L^2$ of a Half-space

Published:2010-07-26
Printed: Mar 2011
• Bassam Shayya,
Department of Mathematics, American University of Beirut, Beirut, Lebanon
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## Abstract

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.
 MSC Classifications: 42B10 - Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 28A75 - Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]

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