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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A sharp estimate for dyadic martingales with multiple indices
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by Gregory J. Morrow PDF
Proc. Amer. Math. Soc. 101 (1987), 705-708 Request permission

Abstract:

A variant of Doob’s maximal inequality is obtained for dyadic martingales with multiple indices. The inequality furnishes a precise estimate of the ${L^p}$ norm of the maximal function in terms of the ${L^p}$ norms of the jumps, $p \geq 2$.
References
  • William Beckner, Inequalities in Fourier analysis, Ann. of Math. (2) 102 (1975), no. 1, 159–182. MR 385456, DOI 10.2307/1970980
  • Christer Borell, On the integrability of Banach space valued Walsh polynomials, SĂ©minaire de ProbabilitĂ©s, XIII (Univ. Strasbourg, Strasbourg, 1977/78) Lecture Notes in Math., vol. 721, Springer, Berlin, 1979, pp. 1–3. MR 544777
  • R. Cairoli, Une inĂ©galitĂ© pour martingales Ă  indices multiples et ses applications, SĂ©minaire de ProbabilitĂ©s, IV (Univ. Strasbourg, 1968/69) Lecture Notes in Mathematics, Vol. 124, Springer, Berlin, 1970, pp. 1–27 (French). MR 0270424
  • R. Gundy, Notes, 1980.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 101 (1987), 705-708
  • MSC: Primary 60G42; Secondary 60G48
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0911037-1
  • MathSciNet review: 911037