On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators

@article{Iosevich2011OnAD,
  title={On angles determined by fractal subsets of the Euclidean space via Sobolev bounds for bi-linear operators},
  author={Alex Iosevich and Mihalis Mourgoglou and Eyvindur Ari Palsson},
  journal={arXiv: Classical Analysis and ODEs},
  year={2011}
}
We prove that if the Hausdorff dimension of a compact subset of ${\mathbb R}^d$ is greater than $\frac{d+1}{2}$, then the set of angles determined by triples of points from this set has positive Lebesgue measure. Sobolev bounds for bi-linear analogs of generalized Radon transforms and the method of stationary phase play a key role. These results complement those of V. Harangi, T. Keleti, G. Kiss, P. Maga, P. Mattila and B. Stenner in (\cite{HKKMMS10}). We also obtain new upper bounds for the… 
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