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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Packing spheres and fractal Strichartz estimates in $ \mathbb{R}^d$ for $ d\geq 3$


Author: Daniel M. Oberlin
Journal: Proc. Amer. Math. Soc. 134 (2006), 3201-3209
MSC (2000): Primary 28A75, 35B45
Published electronically: May 11, 2006
MathSciNet review: 2231903
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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.


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Additional Information

Daniel M. Oberlin
Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
Email: oberlin@math.fsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08356-0
PII: S 0002-9939(06)08356-0
Keywords: Spherical averages, Hausdorff dimension, Strichartz estimate
Received by editor(s): May 10, 2005
Published electronically: May 11, 2006
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.