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Proceedings of the American Mathematical Society

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A martingale inequality related to exponential square integrability


Author: Jill Pipher
Journal: Proc. Amer. Math. Soc. 118 (1993), 541-546
MSC: Primary 42B25
DOI: https://doi.org/10.1090/S0002-9939-1993-1131038-3
MathSciNet review: 1131038
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Abstract: We present an inequality for dyadic martingales (together with its continuous analog for functions on $ {\mathbb{R}^n}$) which is shown to be equivalent to a result of Chang-Wilson-Wolff on exponential square integrability. The analog of this weighted inequality for double dyadic martingales is also proven. Finally, we discuss a possible connection between these inequalities and a theorem of Garnett.


References [Enhancements On Off] (What's this?)

  • [1] S.-Y. A. Chang, J. M. Wilson, and T. H. Wolff, Some weighted norm inequalities for the Schrödinger operator, Comment. Math. Helv. 60 (1985), 217-246. MR 800004 (87d:42027)
  • [2] R Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. MR 0358205 (50:10670)
  • [3] B. E. J. Dahlberg, Approximation of harmonic functions, Ann. Inst. Fourier (Grenoble) 30 (1980), 97-107. MR 584274 (82i:31010)
  • [4] C. Fefferman and E. Stein, $ {H^p}$ spaces of several variables, Acta Math. 129 (1972), 137-192. MR 0447953 (56:6263)
  • [5] J. Garnett, Two constructions in $ BMO$, Proc. Sympos. Pure Math., vol. 35, Amer. Math. Soc., Providence, RI, 1979, pp. 295-301. MR 545269 (81d:30058)
  • [6] J. Pipher, Bounded double square functions, Ann. Inst. Fourier (Grenoble) 36 (1986), 69-82. MR 850744 (88h:42021)
  • [7] J. M. Wilson, Weighted inequalities for the dyadic square function without dyadic $ {A_\infty }$, Duke Math. J. 55 (1987), 19-50. MR 883661 (88d:42034)
  • [8] -, A sharp inequality for the square function, Duke Math. J. 55 (1987), 879-888. MR 916125 (89a:42029)
  • [9] A. Wald, Sequential analysis, Wiley, New York, 1974. MR 0020764 (8:593h)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1131038-3
Article copyright: © Copyright 1993 American Mathematical Society

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