Skip to main content

Inegalites pour martingales a un et deux indices: L’espace Hp

Part of the Lecture Notes in Mathematics book series (LNMECOLE,volume 774)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. AUSTIN, D. G., A sample function property of martingales, Ann. Math. Statist. 37(1966), 1396–1397.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. BESICOVITCH, A. S. On a general metric property of summable functions. J. London Math. Soc. 1(1926), 120–128.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. BURKHOLDER, D. L. Martingale transforms. Ann. Math. Statist. 37 (1966), 1494–1504.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. BURKHOLDER, D. L., GUNDY, R. F. Extrapolation and interpolation of quasilinear operators on martingales. Acta Math. 124 (1970), 249–304.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. _____ Distribution function inequalities for the area integral. Studia Math. 44 (1972), 527–544.

    MathSciNet  MATH  Google Scholar 

  6. _____ Boundary behavior of harmonic functions in a half-space and Brownian motion. Ann. Inst. Fourier (Grenoble) 23 (1973), 195–212.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. BURKHOLDER, D. L., DAVIS, B. J., GUNDY, R. F. Integral inequalities for convex functions of operators on martingales. Proc. Sixth Berkeley Symposium Math. Statist. and Probability 2 (1972), 223–240.

    MathSciNet  MATH  Google Scholar 

  8. BURKHOLDER, D. L., GUNDY, R. F., SILVERSTEIN, M. L. A maximal function characterization of the class Hp. Trans. Amer. Math. Soc. 157 (1971), 137–153.

    MathSciNet  MATH  Google Scholar 

  9. CAIROLI, R. Une inégalité pour martingales à indices multiples et des applications. Sém. Probabilités IV (Univ. Strasbourg 1968/69). Lecture Notes in Math. vol. 124, Springer Verlag, Berlin (1970), 1–27.

    MATH  Google Scholar 

  10. CAIROLI, R., WALSH, J. B. Stochastic integrals in the plane. Acta Math. 134 (1975), 111–183.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. CALDERÓN, A. P. On a theorem of Marcinkiewicz and Zygmund. Trans. Amer. Math. Soc. 68 (1950), 55–61.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. _____ On the behavior of harmonic functions at the boundary. Trans. Amer. Math. Soc. 68 (1950), 47–54.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. _____ Commutators of singular integrals. Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1092–1099.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. CALDERÓN, A. P., ZYGMUND, A. On the existence of certain singular integrals. Ann. Math. 88 (1952), 85–139.

    MathSciNet  MATH  Google Scholar 

  15. CHAO, J. A., TAIBLESON, M. H. A subregularity inequality for conjugate systems on local fields. Studia Math. 46 (1973), 249–257.

    MathSciNet  MATH  Google Scholar 

  16. COIFMAN, R. R., FEFFERMAN, C. Weighted norm inequalities for maximal functions and singular integrals. Studia Math. 51 (1974), 241–250.

    MathSciNet  MATH  Google Scholar 

  17. DAVIS, B. On the integrability of the martingale square function. Israël J. Math. 8 (1970), 187–190.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. DAVIS, B. An inequality for the distribution of the Brownian gradient function. Proc. Amer. Math. Soc. 37 (1973), 189–194.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. DOOB, J. L. Stochastic processes. Wiley, New York, 1953.

    MATH  Google Scholar 

  20. FEFFERMAN, C. Characterization of bounded mean oscillation. Bull. Amer. Math. Soc. 77 (1971), 587–588.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. FEFFERMAN, C., STEIN, E. M. Hp spaces of several variables. Acta Math. 129 (1972), 137–193.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. GUNDY, R. F. A decomposition for L1-bounded martingales. Ann. Math. Statist. 39 (1938), 134–138.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. GUNDY, R. F., VAROPOULOS, N. Th. A martingale that occurs in harmonic analysis. Ark. Math. 14 (1976), 2, 179–187.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. GUNDY, R. F., WHEEDEN, R. L. Weighted norm inequalities for the non-tangential maximal function, Lusin area integral, Walsh-Paley series. Studia Math. 49 (1974), 107–124.

    MathSciNet  MATH  Google Scholar 

  25. HARDY, G. H. The mean value of the modulus of an analytic function. Proc. London Math. Soc. 12 (1913), 365–372.

    CrossRef  Google Scholar 

  26. HARDY, C. H., LITTLEWOOD, J. E. A maximal theorem with function theoretic applications. Acta Math. 54 (1930), 81–116.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. JANSON, S. Characterization of H1 by singular integral transforms on martingales and Rn. Math. Scand. 41 (1977), 140–152.

    MathSciNet  MATH  Google Scholar 

  28. JESSEN, B., MARCINKIEWICZ, J., ZYGMUND, A. Note on the differentiability of multiple integrals. Fund. Math. 25 (1935), 217–234.

    MATH  Google Scholar 

  29. MALLIAVIN, M.-P. et MALLIAVIN, P. Intégrales de Lusin-Calderón pour les fonctions biharmoniques. Bull. Sc. Math. 101 (1977), 357–384.

    MathSciNet  MATH  Google Scholar 

  30. MARCINKIEWICZ, J. Collected papers.

    Google Scholar 

  31. MUCKENHOUPT, B. M. Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc. 165 (1972), 207–226.

    CrossRef  MathSciNet  MATH  Google Scholar 

  32. PALEY, R.E.A.C. A remarkable series of orthogonal functions I. Proc. London Math. Soc. 34 (1932), 241–264.

    CrossRef  MathSciNet  MATH  Google Scholar 

  33. RIESZ, F. Über die Randwerte einer analytischen Funktion. Math. Zeit. 18 (1923), 87–95.

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. RIESZ, F.-M. Über Randewerte einer analytischen Funktion. Quatrième congrès math. scand. Stockholm (1916), 27–44.

    Google Scholar 

  35. RIESZ, M. Sur les fonctions conjuguées. Math. Zeit. 27 (1927), 218–244.

    CrossRef  MathSciNet  MATH  Google Scholar 

  36. GUNDY, R.F. and STEIN E.M. Proc. Nat. Acad. Sci. (U.S.A.) 76 (1979), 3, 1026–1029.

    CrossRef  MathSciNet  Google Scholar 

  37. STEIN, E. M., WEISS, G. On the theory of harmonic functions of several variables, I. The theory of HP-spaces. Acta Math. 103(1960), 25–62.

    CrossRef  MathSciNet  MATH  Google Scholar 

  38. TAIBLESON, M. H. Fourier analysis on local fields. Math. notes, Princeton Univ. Press, Princeton 1975.

    MATH  Google Scholar 

  39. YANO, S., On a lemma of Marcinkiewicz and its applications to Fourier series, Tohoku Math. J. 11(1959), 191–215.

    CrossRef  MathSciNet  MATH  Google Scholar 

  40. ZYGMUND, A. Trigonometric series. Vol. I, II, 2nd ed. Cambridge Univ. Press, Cambridge, 1968.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Gundy, R.F. (1980). Inegalites pour martingales a un et deux indices: L’espace Hp . In: Hennequin, P.L. (eds) Ecole d’Eté de Probabilités de Saint-Flour VIII-1978. Lecture Notes in Mathematics, vol 774. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089625

Download citation

  • DOI: https://doi.org/10.1007/BFb0089625

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09741-9

  • Online ISBN: 978-3-540-38567-7

  • eBook Packages: Springer Book Archive