# 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}
}
• Published 31 October 2011
• Mathematics
• arXiv: Classical Analysis and ODEs
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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This book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other
Background 1. Stationary phase 2. Non-homogeneous oscillatory integral operators 3. Pseudo-differential operators 4. The half-wave operator and functions of pseudo-differential operators 5. Lp