Pointwise ergodic theorems for radial averages on simple Lie groups I

previous :: next

Pointwise ergodic theorems for radial averages on simple Lie groups I

Amos Nevo

Source: Duke Math. J. Volume 76, Number 1 (1994), 113-140.

First Page: Show

Related Works:

See also: Amos Nevo. Pointwise ergodic theorems for radial averages on simple Lie groups II. Duke Math. J. Vol. 86, No. 2 (1997), pp. 239–259.

Project Euclid: euclid.dmj/1077242666

See also: R. C. Vaughan, T. D. Wooley. Further improvements in Waring’s problem, III: Eighth powers. Philos. Trans. Roy. Soc. London Ser. A 345 (1993), pp. 385–396.

Mathematical Reviews (MathSciNet): MR1253500

Primary Subjects: 28D15

Secondary Subjects: 22D40, 22E46, 43A80

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/1077286741
Mathematical Reviews number (MathSciNet): MR1301188
Zentralblatt MATH identifier: 0838.43013
Digital Object Identifier: doi:10.1215/S0012-7094-94-07605-9

back to Table of Contents

References

[B] 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

[Ca] A. P. Calderón, Ergodic theory and translation-invariant operators, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 349–353.

Mathematical Reviews (MathSciNet): MR37:2939

Zentralblatt MATH: 0185.21806

Digital Object Identifier: doi:10.1073/pnas.59.2.349

JSTOR: links.jstor.org

[CS] J. L. Clerc and E. M. Stein, $L\spp$-multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911–3912.

Mathematical Reviews (MathSciNet): MR51:3803

Zentralblatt MATH: 0296.43004

Digital Object Identifier: doi:10.1073/pnas.71.10.3911

JSTOR: links.jstor.org

[DRS] W. Duke, Z. Rudnick, and P. Sarnak, Density of integer points on affine homogeneous varieties, Duke Math. J. 71 (1993), no. 1, 143–179.

Mathematical Reviews (MathSciNet): MR94k:11072

Zentralblatt MATH: 0798.11024

Digital Object Identifier: doi:10.1215/S0012-7094-93-07107-4

Project Euclid: euclid.dmj/1077289840

[EM] A. Eskin and C. McMullen, Mixing, counting, and equidistribution in Lie groups, Duke Math. J. 71 (1993), no. 1, 181–209.

Mathematical Reviews (MathSciNet): MR95b:22025

Zentralblatt MATH: 0798.11025

Digital Object Identifier: doi:10.1215/S0012-7094-93-07108-6

Project Euclid: euclid.dmj/1077289841

[Fa] J. Faraut, Analyse harmonique sur la paires de Guelfand les espaces hyperboliques, Analyse Harmonique ed. P. Eymard, Le Cours du C.I.M.P.A., Nancy, 1980.

[FJK] M. Flensted-Jensen and T. H. Koornwinder, Positive definite spherical functions on a noncompact, rank one symmetric space, Analyse harmonique sur les groupes de Lie (Sém., Nancy-Strasbourg 1976–1978), II, Lecture Notes in Math., vol. 739, Springer, Berlin, 1979, pp. 249–282.

Mathematical Reviews (MathSciNet): MR81j:43015

Zentralblatt MATH: 0433.43014

Digital Object Identifier: doi:10.1007/BFb0062495

[F] H. Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. of Math. (2) 77 (1963), 335–386.

Mathematical Reviews (MathSciNet): MR26:3820

Zentralblatt MATH: 0192.12704

Digital Object Identifier: doi:10.2307/1970220

JSTOR: links.jstor.org

[FKW] H. Furstenberg, Y. Katznelson, and B. Weiss, Ergodic theory and configurations in sets of positive density, Mathematics of Ramsey theory eds. J. Nešetřil and V. Rödl, Algorithms Combin., vol. 5, Springer, Berlin, 1990, pp. 184–198.

Mathematical Reviews (MathSciNet): MR1083601

Zentralblatt MATH: 0738.28013

[GV] R. Gangolli and V. S. Varadarajan, Harmonic analysis of spherical functions on real reductive groups, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 101, Springer-Verlag, Berlin, 1988.

Mathematical Reviews (MathSciNet): MR89m:22015

Zentralblatt MATH: 0675.43004

[HC1] Harish-Chandra, Spherical functions on a semisimple Lie group. I, Amer. J. Math. 80 (1958), 241–310.

Mathematical Reviews (MathSciNet): MR20:925

Zentralblatt MATH: 0093.12801

Digital Object Identifier: doi:10.2307/2372786

JSTOR: links.jstor.org

[HC2] Harish-Chandra, Spherical functions on a semisimple Lie group. II, Amer. J. Math. 80 (1958), 553–613.

Mathematical Reviews (MathSciNet): MR21:92

Zentralblatt MATH: 0093.12801

Digital Object Identifier: doi:10.2307/2372772

JSTOR: links.jstor.org

[He1] S. Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1978.

Mathematical Reviews (MathSciNet): MR80k:53081

Zentralblatt MATH: 0451.53038

[He2] S. Helgason, Groups and geometric analysis, Pure and Applied Mathematics, vol. 113, Academic Press Inc., Orlando, FL, 1984.

Mathematical Reviews (MathSciNet): MR86c:22017

Zentralblatt MATH: 0543.58001

[HM] R. E. Howe and C. C. Moore, Asymptotic properties of unitary representations, J. Funct. Anal. 32 (1979), no. 1, 72–96.

Mathematical Reviews (MathSciNet): MR80g:22017

Zentralblatt MATH: 0543.58001

Digital Object Identifier: doi:10.1016/0022-1236(79)90078-8

[J] R. Jones, Ergodic averages on spheres, to appear in J. Analyse Math.

Mathematical Reviews (MathSciNet): MR1253437

Zentralblatt MATH: 0828.28007

Digital Object Identifier: doi:10.1007/BF02788837

[N1] A. Nevo, Pointwise ergodic theorems for radial averages on simple Lie groups II, preprint.

Mathematical Reviews (MathSciNet): MR1430433

Zentralblatt MATH: 0869.43005

Digital Object Identifier: doi:10.1215/S0012-7094-97-08607-5

Project Euclid: euclid.dmj/1077242666

[N2] A. Nevo, Harmonic analysis and pointwise ergodic theorems for non-commuting transformations, to appear in J. Amer. Math. Soc.

Mathematical Reviews (MathSciNet): MR1266737

Zentralblatt MATH: 0812.22005

Digital Object Identifier: doi:10.2307/2152735

JSTOR: links.jstor.org

[NS] A. Nevo and E. M. Stein, A generalization of Birkhoff's pointwise ergodic theorem, to appear in Acta Math.

Mathematical Reviews (MathSciNet): MR1294672

Zentralblatt MATH: 0837.22003

Digital Object Identifier: doi:10.1007/BF02392571

[Pe] K. Petersen, Ergodic theory, Cambridge Studies in Advanced Mathematics, vol. 2, Cambridge University Press, Cambridge, 1983.

Mathematical Reviews (MathSciNet): MR87i:28002

Zentralblatt MATH: 0507.28010

[R] A. Ramsay, Measurable group actions are essentially Borel actions, Israel J. Math. 51 (1985), no. 4, 339–346.

Mathematical Reviews (MathSciNet): MR87e:28035

Zentralblatt MATH: 0605.28010

Digital Object Identifier: doi:10.1007/BF02764724

[S1] E. M. Stein, On the maximal ergodic theorem, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1894–1897.

Mathematical Reviews (MathSciNet): MR24:A1367

Zentralblatt MATH: 0182.47102

Digital Object Identifier: doi:10.1073/pnas.47.12.1894

JSTOR: links.jstor.org

[S2] E. M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J., 1970.

Mathematical Reviews (MathSciNet): MR40:6176

Zentralblatt MATH: 0193.10502

[S3] E. M. Stein, Maximal functions. II. Homogeneous curves, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2176–2177.

Mathematical Reviews (MathSciNet): MR54:8133b

Zentralblatt MATH: 0332.42019

Digital Object Identifier: doi:10.1073/pnas.73.7.2176

JSTOR: links.jstor.org

[S4] E. M. Stein, Maximal functions: Poisson integrals on symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 8, 2547–2549.

Mathematical Reviews (MathSciNet): MR54:8133c

Zentralblatt MATH: 0332.43012

Digital Object Identifier: doi:10.1073/pnas.73.8.2547

JSTOR: links.jstor.org

[SW] E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239–1295.

Mathematical Reviews (MathSciNet): MR80k:42023

Zentralblatt MATH: 0393.42010

Digital Object Identifier: doi:10.1090/S0002-9904-1978-14554-6

Project Euclid: euclid.bams/1183541467

[Str] J.-O. Strömberg, Weak type $L\sp1$ estimates for maximal functions on noncompact symmetric spaces, Ann. of Math. (2) 114 (1981), no. 1, 115–126.

Mathematical Reviews (MathSciNet): MR82k:43010

Zentralblatt MATH: 0472.43010

Digital Object Identifier: doi:10.2307/1971380

JSTOR: links.jstor.org

[T] E. C. Tichmarsh, The Theory of Functions, 2nd edition, Oxford University Press, Oxford, 1939.

[V] V. S. Varadarajan, Groups of automorphisms of Borel spaces, Trans. Amer. Math. Soc. 109 (1963), 191–220.

Mathematical Reviews (MathSciNet): MR28:3139

Zentralblatt MATH: 0192.14203

Digital Object Identifier: doi:10.2307/1993903

JSTOR: links.jstor.org

[Wa] S. Wainger, Averages and singular integrals over lower-dimensional sets, Beijing lectures in harmonic analysis (Beijing, 1984) ed. E. M. Stein, Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 357–421.

Mathematical Reviews (MathSciNet): MR89a:42026

Zentralblatt MATH: 0627.42006

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?