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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, 28A75 show english descriptions Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
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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