Skip to main content
SpringerLink
Log in

Almost everywhere convergence of weighted averages

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Akcoglu, M., del Junco, A.: Convergence of averages of point transformations. Proc. Am. Math. Soc.49, 265–266 (1975)

    Google Scholar 

  2. Bellow, A., Losert, V.: The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences. Trans. Am. Math. Soc.288, 307–345 (1985)

    Google Scholar 

  3. Bellow, A., Jones, R., Rosenblatt, J.: Convergence for moving averages. Ergodic Theory Dyn. Syst.10, 43–62 (1990)

    Google Scholar 

  4. Bourgain, J.: On the maximal ergodic theorem for certain subsets of the integers. Isr. J. Math.61, 39–72 (1988)

    Google Scholar 

  5. Calderón, A.P.: Ergodic theory and translation-invariant operators. Proc. Natl. Acad. Sci. USA59, 349–353 (1968)

    Google Scholar 

  6. Déniel, Y.: On a.s. Cesàro-α convergence for stationary or orthogonal random variables. J. Theor. Probab.2, 475–485 (1989)

    Google Scholar 

  7. Duoandikoetxea, J., Rubio de Francia, J.: Maximal and singular integral operators via Fourier transform estimates. Invent. Math.84, 541–561 (1986)

    Google Scholar 

  8. Derriennic, Y.: Personal communication

  9. Emerson, W.R.: The pointwise ergodic theorem for amenable groups. Am. J. Math.96, 472–487 (1974)

    Google Scholar 

  10. Foguel, S.R.: On iterates of convolutions. Proc. Am. Math. Soc.47, 368–370 (1975)

    Google Scholar 

  11. Foguel, S.R.: Iterates of a convolution on a non-abelian group. Ann. Inst. Henri Poincaré11, 199–202 (1975)

    Google Scholar 

  12. Huang, Y.: Random sets for the pointwise ergodic theorem. Ph.d. Thesis, Northwestern University: 1989

  13. Kahane, J.-P.: Some random series of functions, 2nd ed. Cambridge: Cambridge University Press 1985

    Google Scholar 

  14. Pier, J.-P.: Amenable locally compact groups. New York: John Wiley and Sons 1984

    Google Scholar 

  15. Petrov, V.V.: Sums of independent random variables. (Ergeb. Math., Grenzgeb., vol. 82) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  16. Rosenblatt, J.: Ergodic and mixing random walks on locally compact groups. Math. Ann.257, 31–42 (1981)

    Google Scholar 

  17. Rosenblatt, J.: Ergodic group actions. Arch. Math.47, 263–269 (1986)

    Google Scholar 

  18. Stein E.M.: On the maximal ergodic theorem. Proc. Natl. Acad. Sci. USA47, 1894–1897 (1961)

    Google Scholar 

  19. Tempelman, A.A.: Ergodic theorems for general dynamical systems. Sov. Math. Dokl.8, 1213–1216 (1967)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Northwestern University, 60201, Evanston, IL, USA

    Alexandra Bellow

  2. Mathematics Department DePaul University, 2219 N. Kenmore, 60614, Chicago, IL, USA

    Roger L. Jones

  3. Mathematics Department, Ohio State University, 43210, Columbus, OH, USA

    Joseph Rosenblatt

Authors
  1. Alexandra Bellow
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roger L. Jones
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Joseph Rosenblatt
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by NSF grant DMS-8910947

Partially supported by NSF grant DMS-8802126

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bellow, A., Jones, R.L. & Rosenblatt, J. Almost everywhere convergence of weighted averages. Math. Ann. 293, 399–426 (1992). https://doi.org/10.1007/BF01444724

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444724

Keywords

Search

Navigation