A geometric proof of the circular maximal theorem
W. Schlag
Source: Duke Math. J. Volume 93, Number 3
(1998), 505-533.
First Page:
Show
Hide
Primary Subjects:
42B25
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077231104
Mathematical Reviews number (MathSciNet): MR1626711
Zentralblatt MATH identifier: 0942.42010
Digital Object Identifier: doi:10.1215/S0012-7094-98-09318-8
References
[1] J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69–85.
Mathematical Reviews (MathSciNet): MR88f:42036
Zentralblatt MATH: 0626.42012
Digital Object Identifier: doi:10.1007/BF02792533
[2] J. Bourgain, On high-dimensional maximal functions associated to convex bodies, Amer. J. Math. 108 (1986), no. 6, 1467–1476.
Mathematical Reviews (MathSciNet): MR88h:42020
Zentralblatt MATH: 0621.42015
Digital Object Identifier: doi:10.2307/2374532
JSTOR: links.jstor.org
[3] A. Córdoba, The Kakeya maximal function and the spherical summation multipliers, Amer. J. Math. 99 (1977), no. 1, 1–22.
Mathematical Reviews (MathSciNet): MR56:6259
Zentralblatt MATH: 0384.42008
Digital Object Identifier: doi:10.2307/2374006
JSTOR: links.jstor.org
[4] A. Córdoba, Maximal functions, covering lemmas and Fourier multipliers, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 1, Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 29–50.
Mathematical Reviews (MathSciNet): MR81f:42017
Zentralblatt MATH: 0472.42010
[5] A. Córdoba and R. Fefferman, A geometric proof of the strong maximal theorem, Ann. of Math. (2) 102 (1975), no. 1, 95–100.
Mathematical Reviews (MathSciNet): MR52:690
Zentralblatt MATH: 0324.28004
Digital Object Identifier: doi:10.2307/1970976
JSTOR: links.jstor.org
[6] H. Federer, Geometric Measure Theory, Grundlehren Math. Wiss., vol. 153, Springer-Verlag, New York, 1969.
Mathematical Reviews (MathSciNet): MR41:1976
Zentralblatt MATH: 0176.00801
[7] L. Kolasa and T. Wolff, On some variants of the Kakeya problem, preprint, 1995, to appear in Pacific J. Math.
Mathematical Reviews (MathSciNet): MR1722768
Zentralblatt MATH: 1019.42013
Digital Object Identifier: doi:10.2140/pjm.1999.190.111
[8] J. M. Marstrand, Packing circles in the plane, Proc. London Math. Soc. (3) 55 (1987), no. 1, 37–58.
Mathematical Reviews (MathSciNet): MR88i:28012
Zentralblatt MATH: 0597.28008
Digital Object Identifier: doi:10.1112/plms/s3-55.1.37
[9] G. Mockenhaupt, A. Seeger, and C. Sogge, Wave front sets, local smoothing and Bourgain's circular maximal theorem, Ann. of Math. (2) 136 (1992), no. 1, 207–218.
Mathematical Reviews (MathSciNet): MR93i:42009
Zentralblatt MATH: 0759.42016
Digital Object Identifier: doi:10.2307/2946549
JSTOR: links.jstor.org
[10] W. Schlag, A generalization of Bourgain's circular maximal theorem, J. Amer. Math. Soc. 10 (1997), no. 1, 103–122.
Mathematical Reviews (MathSciNet): MR97c:42035
Zentralblatt MATH: 0867.42010
Digital Object Identifier: doi:10.1090/S0894-0347-97-00217-8
JSTOR: links.jstor.org
[11] W. Schlag, $L^p\rightarrow L^q$ estimates for the circular maximal function, Ph.D. thesis, California Institute of Technology, 1996.
[12] W. Schlag and C. Sogge, Local smoothing estimates related to the circular maximal theorem, Math. Res. Lett. 4 (1997), no. 1, 1–15.
Mathematical Reviews (MathSciNet): MR98e:42018
Zentralblatt MATH: 0877.42006
[13] C. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), no. 2, 349–376.
Mathematical Reviews (MathSciNet): MR92i:58192
Zentralblatt MATH: 0754.35004
Digital Object Identifier: doi:10.1007/BF01245080
[14] E. Stein, Maximal functions, I: Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175.
Mathematical Reviews (MathSciNet): MR54:8133a
Zentralblatt MATH: 0332.42018
Digital Object Identifier: doi:10.1073/pnas.73.7.2174
JSTOR: links.jstor.org
[15] T. Wolff, A Kakeya-type problem for circles, Amer. J. Math. 119 (1997), no. 5, 985–1026.
Mathematical Reviews (MathSciNet): MR98m:42027
Zentralblatt MATH: 0892.52003
Digital Object Identifier: doi:10.1353/ajm.1997.0034
Duke Mathematical Journal
