ArticleOriginal scientific text

Title

On ergodic singular integral operators

Authors 1, 1

Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kanpur, Kanpur-208016, India

Bibliography

  1. E. Berkson, T. A. Gillespie and P. S. Muhly, Abstract spectral decompositions guaranteed by the Hilbert transform, Proc. London Math. Soc. (3) 53 (1986), 489-517.
  2. J. Bourgain, Some remarks on Banach spaces in which martingale difference sequences are unconditional, Ark. Mat. 21 (1983), 163-168.
  3. J. Bourgain, Extension of a result of Benedek, Calderón and Panzone, ibid. 22 (1984), 91-95.
  4. D. L. Burkholder, A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions, in: Conf. on Harmonic Analysis in Honor of A. Zygmund (Chicago, Ill., 1981), Wadsworth, Belmont, Calif., 1983, 270-286.
  5. D. L. Burkholder, A geometric characterization of UMD Banach spaces, Ann. Probab. 9 (1981), 997-1011.
  6. A. P. Calderón, Ergodic theory and translation invariant operators, Proc. Nat. Acad. Sci. U.S.A. 59 (1968), 349-353.
  7. R. R. Coifman and G. Weiss, Transference Methods in Analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., 1977.
  8. M. Cotlar, A unified theory of Hilbert transform and ergodic theorems, Rev. Mat. Cuyana 1 (1955), 105-167.
  9. J. Diestel and J. J. Uhl, Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.
  10. R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, 1977.
  11. K. Petersen, Another proof of the existence of the ergodic Hilbert transform, Proc. Amer. Math. Soc. 88 (1983), 39-43.
  12. J. L. Rubio de Francia, F. J. Ruiz and J. L. Torrea, Calderón-Zygmund theory of operator-valued kernels, Adv. in Math. 62 (1986), 7-48.
  13. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970.
  14. A. Torchinsky, Real-Variable Methods in Harmonic Analysis, Academic Press, 1986.
Pages:
299-307
Main language of publication
English
Received
1992-05-26
Accepted
1993-04-15
Published
1993
Exact and natural sciences