### SPHERICAL MEANS AND PINNED DISTANCE SETS

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Oberlin, Daniel;Oberlin, Richard

• 투고 : 2014.11.14
• 발행 : 2015.01.31
• 5 3

#### 초록

We use mixed norm estimates for the spherical averaging operator to obtain some results concerning pinned distance sets.

#### 키워드

spherical averaging operator;Hausdorff dimension;pinned distance set

#### 참고문헌

1. T. Mitsis, Spherical means and measures with finite energy, Colloq. Math. 114 (2009), no. 1, 9-13. https://doi.org/10.4064/cm114-1-2
2. D. Oberlin, Restricted Radon transforms and projections of planar sets, Canad. Math. Bull. 55 (2012), no. 4, 815-820. https://doi.org/10.4153/CMB-2011-064-6
3. D. Oberlin, Packing spheres and fractal Strichartz estimates in ${\mathbb{R}^d}$ for $d{\succeq}3$, Proc. Amer. Math. Soc. 134 (2006), no. 11, 3201-3209. https://doi.org/10.1090/S0002-9939-06-08356-0
4. D. Oberlin, Unions of hyperplanes, unions of spheres, and some related estimates, Illinois J. Math. 51 (2007), no. 4, 1265-1274.
5. Y. Peres and W. Schlag, Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions, Duke Math. J. 102 (2000), no. 2, 193-251. https://doi.org/10.1215/S0012-7094-00-10222-0
6. T.Wolff, Local smoothing type estimates on $L^p$ for large p, Geom. Funct. Anal. 10 (2000), no. 5, 1237-1288. https://doi.org/10.1007/PL00001652

#### 과제정보

연구 과제 주관 기관 : NSF