1. CMB 2011 (vol 56 pp. 326)
|Restricting Fourier Transforms of Measures to Curves in $\mathbb R^2$|
We establish estimates for restrictions to certain curves in $\mathbb R^2$ of the Fourier transforms of some fractal measures.
Keywords:Fourier transforms of fractal measures, Fourier restriction
2. CMB 2010 (vol 54 pp. 172)
|Measures with Fourier Transforms in $L^2$ of a Half-space|
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.
3. CMB 2005 (vol 48 pp. 260)
|A Restriction Theorem for a \\$k$-Surface in $\mathbb R ^n$ |
We establish a sharp Fourier restriction estimate for a measure on a $k$-surface in $\mathbb R ^n$, where $n=k(k+3)/2$.