|
Packing spheres and fractal Strichartz estimates in  for 
Author(s):
Daniel
M.
Oberlin
Journal:
Proc. Amer. Math. Soc.
134
(2006),
3201-3209.
MSC (2000):
Primary 28A75, 35B45
Posted:
May 11, 2006
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove an estimate for the spherical average operator in  if  . 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:
-
- 1.
- J. Bourgain Besicovitch type maximal operators and applications to Fourier analysis, Geometric and Functional Analysis 1 (1991), 147-187. MR 1097257 (92g:42010)
- 2.
- B. Erdogan A note on the Fourier transform of fractal measures, Math. Res. Lett. 11 (2004), 299-313. MR 2067475 (2005j:42008)
- 3.
- T. Mitsis On a problem related to sphere and circle packing, J. London Math. Soc. 60 (1999), 501-516. MR 1724841 (2001f:28008)
- 4.
- D. Oberlin
 mapping properties of the Radon transform, Springer Lecture Notes in Mathematics 995 (1983), 95-102. MR 0717229 (85j:44005) - 5.
- D. Oberlin An estimate for a restricted X-ray transform, Canadian Math. Bull. 43 (2000), 472-476. MR 1793949 (2001k:44004)
- 6.
- D. Oberlin Restricted Radon transforms and unions of hyperplanes Rev. Mat. Iberoamericana, to appear.
- 7.
- E. M. Stein Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals,
Princeton University Press, 1993. MR 1232192 (95c:42002) - 8.
- M. Talagrand Sur la mesure de la projection d'un compact et certaines familles de cercles, Bull. Sci. Math. 104 (1980), 225-231. MR 0592470 (82b:28004)
- 9.
- T. Wolff Local smoothing estimates on
 for large  , Geometric and Functional Analysis 10 (2000), 1237-1288. MR 1800068 (2001k:42030)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
28A75, 35B45
Retrieve articles in all Journals with MSC
(2000):
28A75, 35B45
Additional Information:
Daniel
M.
Oberlin
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510
Email:
oberlin@math.fsu.edu
DOI:
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
Posted:
May 11, 2006
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
Comments: webmaster@ams.org