Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SPHERICAL MEANS AND PINNED DISTANCE SETS

  • Received : 2014.11.14
  • Published : 2015.01.31
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Abstract

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

Keywords

References

  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

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  1. An L2-identity and pinned distance problem pp.1420-8970, 2019, https://doi.org/10.1007/s00039-019-00482-8