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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Packing spheres and fractal Strichartz estimates in $\mathbb {R}^d$ for $d\geq 3$
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by Daniel M. Oberlin
Proc. Amer. Math. Soc. 134 (2006), 3201-3209
DOI: https://doi.org/10.1090/S0002-9939-06-08356-0
Published electronically: May 11, 2006
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Abstract:

We prove an estimate for the spherical average operator in $\mathbb {R}^d$ if $d\geq 3$. This leads to a lower bound for the Hausdorff dimension of unions of certain collections of spheres and to a Strichartz-type estimate for solutions of the wave equation.
References
  • J. Bourgain, Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal. 1 (1991), no.ย 2, 147โ€“187. MR 1097257, DOI 10.1007/BF01896376
  • M. Burak Erdogฬƒan, A note on the Fourier transform of fractal measures, Math. Res. Lett. 11 (2004), no.ย 2-3, 299โ€“313. MR 2067475, DOI 10.4310/MRL.2004.v11.n3.a3
  • T. Mitsis, On a problem related to sphere and circle packing, J. London Math. Soc. (2) 60 (1999), no.ย 2, 501โ€“516. MR 1724841, DOI 10.1112/S0024610799007838
  • Daniel M. Oberlin, $L^{p}-L^{q}$ mapping properties of the Radon transform, Banach spaces, harmonic analysis, and probability theory (Storrs, Conn., 1980/1981) Lecture Notes in Math., vol. 995, Springer, Berlin, 1983, pp.ย 95โ€“102. MR 717229, DOI 10.1007/BFb0061889
  • Daniel M. Oberlin, An estimate for a restricted X-ray transform, Canad. Math. Bull. 43 (2000), no.ย 4, 472โ€“476. MR 1793949, DOI 10.4153/CMB-2000-055-8
  • D. Oberlin Restricted Radon transforms and unions of hyperplanes Rev. Mat. Iberoamericana, to appear.
  • Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
  • Michel Talagrand, Sur la mesure de la projection dโ€™un compact et certaines familles de cercles, Bull. Sci. Math. (2) 104 (1980), no.ย 3, 225โ€“231 (French, with English summary). MR 592470
  • T. Wolff, Local smoothing type estimates on $L^p$ for large $p$, Geom. Funct. Anal. 10 (2000), no.ย 5, 1237โ€“1288. MR 1800068, DOI 10.1007/PL00001652
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Bibliographic Information
  • Daniel M. Oberlin
  • Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
  • Email: oberlin@math.fsu.edu
  • Received by editor(s): May 10, 2005
  • Published electronically: May 11, 2006
  • Communicated by: Michael T. Lacey
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3201-3209
  • MSC (2000): Primary 28A75, 35B45
  • DOI: https://doi.org/10.1090/S0002-9939-06-08356-0
  • MathSciNet review: 2231903