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Extrapolation and interpolation of quasi-linear operators on martingales

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References

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

    MATH  MathSciNet  Google Scholar 

  2. Calderón, A. P. &Zygmund, A., A note on the interpolation of sublinear operations.Amer. J. Math., 78 (1956), 282–288.

    Article  MATH  MathSciNet  Google Scholar 

  3. Chow, Y. S., Convergence of sums of squares of martingale differences.Ann. Math. Statist., 39 (1968), 123–133.

    MATH  MathSciNet  Google Scholar 

  4. Davis, B., Divergence properties of some martingale transforms.Ann. Math. Statist., 40 (1969), 1852–1854.

    MATH  Google Scholar 

  5. Doob, J. L.,Stochastic processes. New York, 1953.

  6. Dvoretzky, A., Personal communication.

  7. Gundy, R. F., The martingale version of a theorem of Marcinkiewicz and Zygmund.Ann. Math. Statist., 38 (1967), 725–734.

    MATH  MathSciNet  Google Scholar 

  8. —, A decomposition forL 1-bounded martingales.Ann. Math. Statist., 39 (1968), 134–138.

    MATH  MathSciNet  Google Scholar 

  9. —, On the classL logL, martingales, and singular integrals.Studia Math., 33 (1969), 109–118.

    MATH  MathSciNet  Google Scholar 

  10. Hardy, G. H., andLittlewood, J. E., A maximal theorem with function-theoretic applications.Acta Math., 54 (1930), 81–116.

    MATH  Google Scholar 

  11. Marcinkiewicz, J., Quelques théorèmes sur les séries orthogonales.Ann. Soc. Polon. Math., 16 (1937), 84–96 (pages 307–318 of theCollected Papers.)

    Google Scholar 

  12. Marcinkiewicz, J. &Zygmund, A., Quelques théorèmes sur les fonctions indépendantes.Studia Math., 7 (1938), 104–120 (pages 374–388 of theCollected Papers of Marcinkiewicz).

    MATH  Google Scholar 

  13. Millar, P. W., Martingale integrals.Trans. Amer. Math. Soc., 133 (1968), 145–166.

    Article  MATH  MathSciNet  Google Scholar 

  14. Paley, R. E. A. C., A remarkable series of orthogonal functions.Proc. London Math. Soc., 34 (1932), 241–279.

    MATH  Google Scholar 

  15. Stein, E. M.,Topics in harmonic analysis related to the Littlewood-Paley theory. Ann. Math. Studies 63. Princeton, 1970.

  16. Tsuchikura, T., Sample properties of martingales and their arithmetic means.Tôhoku Math. J., 20 (1968), 400–415.

    MATH  MathSciNet  Google Scholar 

  17. Zygmund, A.,Trigonometric series, 2nd edition. Cambridge, 1959.

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The research of the first-named author was supported in part by the Center for Advanced Study of the University of Illinois and by the National Science Foundation under grant GP-8727.

The research of the second-named author was supported in part by the Research Council of Rutgers University while the author was in residence at the University of Illinois (summer 1968) and the Hebrew University of Jerusalem (academic year 1968–69) and by the National Science Foundation under grant GP-8056.

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Burkholder, D.L., Gundy, R.F. Extrapolation and interpolation of quasi-linear operators on martingales. Acta Math. 124, 249–304 (1970). https://doi.org/10.1007/BF02394573

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