Circular averages and Falconer/Erdös distance conjecture in the plane for random metrics

Steve Hofmann, Alex Iosevich

Type: Article

Publication Date: 2004-07-22

Citations: 49

DOI: https://doi.org/10.1090/s0002-9939-04-07603-8

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Locations

Proceedings of the American Mathematical Society - View

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Works That Cite This (48)

Action	Title	Year	Authors
+	Sharpness of Falconer's estimate in continuous and arithmetic settings, geometric incidence theorems and distribution of lattice points in convex domains	2010	Alex Iosevich Steven Senger
+	EXPLORATIONS OF THE ERD } OS-FALCONER DISTANCE PROBLEM AND RELATED APPLICATIONS	2011	Steven Senger Alex Iosevich
+	On sets of directions determined by subsets of ${\Bbb R}^d$	2010	Alex Iosevich Mihalis Mourgoglou Steven Senger
+	Multilinear generalized Radon transforms and point configurations	2012	Loukas Grafakos Allan Greenleaf Alex Iosevich Eyvindur A. Palsson
+	On three point configurations determined by subsets of the Euclidean plane, the associated bilinear operator and applications to discrete geometry	2010	Allan Greenleaf Alex Iosevich
+	None	2005	M. Burak Erdoğan
+	Three-point configurations determined by subsets of $\mathbb{F}_q^2$ via the Elekes-Sharir paradigm	2012	Michael A. Bennett Alex Iosevich Jonathan Pakianathan
+	On distance measures for well-distributed sets	2006	Alex Iosevich Misha Rudnev
+	On sets of directions and angles determined by subsets of ${\Bbb R}^d$	2010	Alex Iosevich Steven Senger Mihalis Mourgoglou
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Works Cited by This (14)

Action	Title	Year	Authors
+	Some Random Series of Functions	1985	Jean‐Pierre Kahane
+	Lectures on Harmonic Analysis	2003	Thomas Wolff
+	None	1999	Thomas Wolff
+	Fourier Integrals in Classical Analysis	2017	Christopher D. Sogge
+	Hausdorff dimension and distance sets	1994	Jean Bourgain
+	Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets	1987	Pertti Mattila
+	Fourier Transforms Related to Convex Sets	1962	Carl Herz
+	Estimates of spherial averages of Fourier transforms and dimensions of sets	1993	Per Sjölin
+	Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions	2000	Yuval Peres Wilhelm Schlag
+	Measure and dimension for some fractal families	1998	Boris Solomyak